#geometry-and-trigonometry

1 messages · Page 346 of 1

lethal sigil
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(b xh) - [4(pi x r^2)/4]

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4/4 = 1

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@sw3atydemon

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@devout cove

near imp
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so this is something new we are learning today and i’m still trying to understand how to go about solving this

trim breach
near imp
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i think whats really throwing me off on this equation is the numbers in the graph for some reason

trim breach
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Along the x-axis, that is actually pretty standard. If you Google the graphs of f(x) = sin(x) and f(x) = cos(x), you might be able to get a feel for how the graphs look and how to apply some of the terms.

near imp
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hm ok i see what you’re saying!

trim breach
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Cool…just ping me back if you get stuck or have any questions!

near imp
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ok thank you for your amazing help!!

abstract prairie
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Can anyone help me with these PES2_EmbarrassedAsk

abstract prairie
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man

meager karma
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do @.helpers

wintry tundra
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circles are hard im sorry ;-;

meager karma
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can u help with this real quick

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i just wanna know if i set it up right and how i would solve that 🧍‍♂️

wintry tundra
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U set it up right

meager karma
wintry tundra
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That's what I'm trying to see

meager karma
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would u do 360/2 to find the base of one of the triangles

wintry tundra
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Nah cuz they aren't split evenly

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Alright I found it

meager karma
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o

wintry tundra
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Ur learning trig?

meager karma
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yeah

wintry tundra
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Cool

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This will be ok then

meager karma
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okok

wintry tundra
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Alright so first u need to find the supplement of the sum of the angles of depression

meager karma
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huh

wintry tundra
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Do u know how to do that

meager karma
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noo we’re learning ab the law of sines and cosines so i think i have to use that

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it’s easy but my brain is dumb so

wintry tundra
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Nah ur fine

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Some people either don't get math off the bat or didn't get taught an optimal way so don't beat urself up

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Anyways let's break down what I said

meager karma
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yeah my teacher isn’t that great lmao

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ok

wintry tundra
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What are the angles of depression

meager karma
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the 72 and 40 degrees

wintry tundra
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Yeah

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So now take the sum of those

meager karma
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so 112 degrees

tiny snow
wintry tundra
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Alright so what is a supplement @meager karma

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With respect to geometry of course

meager karma
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i have no idea 🏃‍♂️🏃‍♂️

wintry tundra
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Oh

meager karma
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HAHA i don’t remember

wintry tundra
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Well a complement is an angle measure that makes another angle 90 degrees or pi/2 radians

meager karma
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ok then

wintry tundra
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A supplement is the same but for 180 degrees or pi radians

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Remember those

meager karma
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okkkk

wintry tundra
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So now find the supplement in degrees of the sum of the angles of depression

meager karma
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bruh

wintry tundra
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Find the supplement of 112

meager karma
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68?

wintry tundra
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Yep

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Nice

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So now the top angle of the large triangle is 68

meager karma
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yes

wintry tundra
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Alright

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Now we gotta use everyone's favorite: parallel lines and transversals

meager karma
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ok how

wintry tundra
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Do u remember interior angle and alternate angles and all those

meager karma
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kinda

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i learned geometry years ago 🧍‍♂️

wintry tundra
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Yeah its needed here

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So because we want to find how high the blimp is, we can say that the blimps height and the ground are parallel

meager karma
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yes

wintry tundra
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Aka the blimp is not approaching the ground or getting higher from the ground

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So I want to find the rightmost angle on the big triangle

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Post the hw again for me

meager karma
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ok

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one sec

wintry tundra
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Alright so let's say the side of the triangle that the 40 is by is infinite and is crossing both the height and the ground

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Then there would be even more angles

meager karma
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okkkk

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so do u want me to find the rest of the missing angles in the whole triangle

wintry tundra
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Well

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I guess but there's more to that

meager karma
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ya so what do we do

wintry tundra
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So this is what would happen with the side

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We want to find the angle with the ? by it

meager karma
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so alt angles for both 72 and 40

wintry tundra
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Yeah

meager karma
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ok

wintry tundra
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Alt int angles

meager karma
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so the angle on the left would be 72 and the right 40

wintry tundra
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👍

meager karma
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yess so now what

wintry tundra
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Now we can split the 68

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So u need to find the complement of 40 and 72

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Complements my bad

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So the comp of 40 then the comp of 72

meager karma
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so for 40 it would be 50

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and for 72 it would be 18?

wintry tundra
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Yep

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And 50 and 18 happen to add up to 68

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How nice

meager karma
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very nice

wintry tundra
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So put 50 and 18 where they belong

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Then we will use trig to get our answer

meager karma
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so which triangle do u wanna use to solve how high the blimp is

wintry tundra
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Doesn't matter

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Whatever works

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But let's use 40 degree triangle bc why not

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Alright so do u remember the law of sines?

meager karma
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uhh yes

wintry tundra
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Well let's use it then

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Wait a sec I might have missed a step lemme check

meager karma
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wait what ab the base of the triangle

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do we need for find that

wintry tundra
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Nvm we are good

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Well we have every angle we need so we can use the law of sines

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To get the sides

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So what angle side pair do we have

meager karma
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it would look like this right

wintry tundra
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Yeah we need the big triangle

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My bad

meager karma
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o

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LMAO my drawing skills

wintry tundra
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Looks fine to me

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Anyways there's only one angle and side that are opposite each other

meager karma
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uhhh

wintry tundra
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What are they?

meager karma
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bruh idk wouldn’t there be multiple that are opposite of each other

wintry tundra
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Nah bc there's only one side that we know of

meager karma
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so would it just be the 68 degrees and 360

wintry tundra
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Yep

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So we want to find the hypotenuse of the 40 triangle

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What angle on the big triangle is opposite to that hypotenuse

meager karma
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would it be 90

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cause it’s a right triangle orrr

wintry tundra
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On the small triangle yes

meager karma
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ok

wintry tundra
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On the big triangle no

meager karma
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oh on the big one

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72

wintry tundra
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Yep

meager karma
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oops

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ok

wintry tundra
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So use law of sines now

meager karma
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so wouldn’t that be x/sin72 and 360/sin68 or am i dumb

wintry tundra
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U are smart

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Bc that's right

meager karma
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yay lol

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ok

wintry tundra
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Man I'm excited to take trig next year with these kinds of problems

meager karma
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why are u excited 😭😭

wintry tundra
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Bc I've already self studied this year so I can breeze thru the class

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But what did u get for x

meager karma
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o ok wait

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so setup would be 360sin72/ sin68 right

wintry tundra
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Yep

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And don't turn that into decimals

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Just keep it like that

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So we can be more accurate

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But now it's time for the last step

meager karma
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wait so it’s 369.27

wintry tundra
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Yes but don't turn it into that yet

meager karma
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o

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how come

wintry tundra
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It's less accurate

meager karma
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so what do we do now

wintry tundra
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Use the small triangle

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Last step time

meager karma
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ok

wintry tundra
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So now we want to find the height which you can use the law of sines for

meager karma
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oh wait so we just solved the hypotenuse of the small triangle rights

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right

wintry tundra
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( sin(72)360 / sin(68) ) / sin 90 = x/sin(40)

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Also yeah we did

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The 40 triangle hypotenuse

meager karma
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man what is that

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yeah^

wintry tundra
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Thats the last thing to do

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But luckily

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guess what sin(90) is

meager karma
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1

wintry tundra
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Mhm

meager karma
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ok so what does that last step do 🏃‍♂️

wintry tundra
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Get the answer

meager karma
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HA ok wait

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so 369.27=x/sin40

wintry tundra
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Don't turn it into decimals

meager karma
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o

wintry tundra
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Keep it as fraction

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Only turn the answer into decimals

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Do u know what to do for the answer?

meager karma
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oh sorry there was a police man at my door LMAO

meager karma
wintry tundra
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It sure would

meager karma
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wow thank u sm this took 68000 years

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ur the best

wintry tundra
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No problem

vivid schooner
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I see congruence because of reflection and the sides of both triangles which I thought was -ss ; not enough info- but the correct answer was -sss congruence-. how?

silent plank
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the triangles share a common side

upper karma
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Any one willing to help me w these?

vast python
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Use Gaussian Elimination can someone walk me through this

dark sparrow
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,rccw

somber coyoteBOT
dark sparrow
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okay so @upper karma @vast python one of you will need to move out of this channel

upper karma
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Oh.. why?

dark sparrow
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you posted your questions within minutes of each other

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and presumably you both want help

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but having that happen in one channel won't do

vast python
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I’ll leave then

dark sparrow
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just go to another channel, there's no need to leave the server outright lol

dark sparrow
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which problem number would you like to start with?

dark sparrow
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uh huh

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so you've done 5 and 6 already, yes?

upper karma
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oh but i fuigured out 9 and 10

upper karma
dark sparrow
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okay

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the concept's the exact same here.

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get the slope of your line by using its perpendicularity to the given line, and then pin down the y-intercept by using the point.

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is something giving you trouble in number 7 that didn't come up in 5 or 6?

dark sparrow
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okay, what is it

upper karma
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oh shoot nvmm i saw what i did i pinned it wrong which got me whole nother answer

dark sparrow
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well then

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i guess that's taken care of

upper karma
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well tyyy

dark sparrow
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anything else?

upper karma
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nope im good😀

dark sparrow
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ok

upper karma
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hi

near imp
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i think i’m overthinking it again but can someone help me with this problem (there’s more like this but this is just one of them i don’t wanna ask for too much)

dense perch
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We know it goes from -pi to 3pi

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So the period is 4pi

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Since it goes 4 to -4 on altitude... the amp is 8/2 or 4

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Btw B would be 2pi / 4pi, or 1/2

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Hope that helps!

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Ping me if you don’t get it por favor, and I’ll try to help

near imp
dense perch
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Np

near imp
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i have 2 more equations like this if it’s alright can you help me with them as well?

dense perch
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Go for it

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I’m bored anyways

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I’ll try my best to help lol

near imp
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here they are lol

dense perch
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Alright, so amplitude is always (highest point - lowest point) /2...

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So the first one goes from 1/2 to -1/2

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A distance of 1

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Divide that by 2 and you have the amp

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For period, we know it goes pi/8 increments

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So it’s distance is 4pi/8 when we count

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And B would hypothetically be 2pi /(4pi/8)

near imp
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hm ok so with the amp would it be 1/2 since we divide the distance by 2?

dense perch
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Yes

near imp
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ok got u

dense perch
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Do you want to try the amp for the second one?

near imp
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i can try!

dense perch
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What do you think it is?

near imp
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i want to say it’s a decimal or fraction because of where it is located where it’s increasing

dense perch
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First: find the max and min values:

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That would be 2 and -2

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We then subtract: 2 - (-2) = 4

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And the amp is 4/2 = 2

near imp
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oh ok i get what you’re saying

dense perch
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Then, for period...

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Increments of pi:

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We go from 1pi to 5pi

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The period would be 4pi as a result...

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And B would hypothetically be 2pi/4pi = 2

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Do you think you get it?

near imp
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so the period in the end would be 2

dense perch
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No...

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Have you learned the equation for these problems yet?

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If not Dw about “B”

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Your answer is 4pi

near imp
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ohhhh wait i get what you’re saying

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sorry i was overthinking it

dense perch
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Nah lol, your good

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It’s really confusing sometimes

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You’re definitely not the only one

near imp
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yeah it is lol but i get what you’re saying thank you for the help!

dense perch
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Np, if you have more questions, feel free to ping me

woeful gyro
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Plz,backup. before i go crazy. How do i go about calculating the angle PQR

dark sparrow
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it... looks like there isn't enough info?

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oh wait no nvm

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there is

tiny snow
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Like we said in another channel...

dark sparrow
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you can just calculate all sides of triangle PQR and apply the law of cosines

tiny snow
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^ that

woeful gyro
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to calculate RP hypotenuse id need an angle to work with? same for hypotenuse QP?

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should i just assumed 90 degrees or what

dark sparrow
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this whole shape is a prism, is it not?

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so presumably the front and right faces are both rectangles

dense perch
woeful gyro
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ok if thats the case, i got RP to 12.8cm and QP to 15.6cm

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i know how to solve angles for 3 sides no angle and 2 sides 1 angle.

dense perch
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Basically, we know all the sides of the face (triangle on the top)

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So use trig to find angle QR”X” on the face

dark sparrow
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do you really need that tho

dense perch
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Use the 180 degrees in a triangle rule to find RQ”X”

dark sparrow
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all you need is the length of RQ, which is just sqrt(12^2 + 8^2)

dense perch
dark sparrow
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yeah but not the one you were talking about.

woeful gyro
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yes, angle PQR

dense perch
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Oh lol, my bad, I just woke up

woeful gyro
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soo assuming my calculations for RP and QP is correct. how to i find myself an angle to work with/ the last side

woeful gyro
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what u do there tho? p^2=12^2+8^2-2* 12*8 *cosp?

dark sparrow
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??

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figuring out RQ is just the pythagorean theorem

woeful gyro
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oh, right.

dark sparrow
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after that, your angle is just $\arccos(\frac{RQ^2 + PQ^2 - RP^2}{2 \cdot RQ \cdot PQ})$

somber coyoteBOT
woeful gyro
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gotcha cheers, the the figure itself makes me confused xd

lament shell
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what did i do wrong?

dark sparrow
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lets see...

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it appears that your only problem is rounding when you weren't asked to

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x should be 10/3, which is not equal to 3.30 exactly.

silent plank
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problem is 4*8 = 32 not 24

lament shell
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yeah im dumb lol

dark sparrow
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or that

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which somehow escaped me lol

dapper bronze
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Need help

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Someone help

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Looking for the angle

trim breach
candid forge
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Can someone explain why e^iθ= cosθ+isinθ intuitively? I understand the proof using Taylor series but I would like a more geometric approach

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I don’t if this is the correct channel to ask that

keen abyss
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Try watching 3b1b s video it's pretty nice

keen abyss
wraith cargo
trim breach
# wraith cargo

Those are similar triangles in 10 since two angles between them are congruent. You can set up a proportion knowing this fact.

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And 11 is an angle bisector problem where you can set up a proportion to solve for x.

wraith cargo
fickle geyser
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yo

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yo

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yo

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do yall know proofs

trim breach
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Someone here can help, so you can just post your question.

lofty granite
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anyone available?

dark sparrow
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no clearly nobody is ever available on this server which hasnt been posted to in 10 years (/massive sarcasm)

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post your question.

lofty granite
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lmao okayyy

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i did 648^2 and got that large ass number

dark sparrow
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648^2?

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why would you do 648^2?

lofty granite
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is the formula not a^2 + b^2 = c^2?

dark sparrow
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it is

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but what you are doing is c = (a^2+b^2)^2 apparently

lofty granite
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wait

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so do i sqaure 648?

dark sparrow
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no! you don't!

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you have c^2 = 648

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this doesn't mean c = 648^2 at all

lofty granite
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ooh

dark sparrow
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you want the opposite of squaring.

lofty granite
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so

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square root it?

mint dune
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~yes~

lofty granite
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oh

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sorry, im still trying to understand trig

mint dune
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at least you're asking questions

lofty granite
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yeah, my teacher is no help lol

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mind if i double check with another question?

fickle prairie
#

Hey everyone! I'm stuck with an analytic geometry problem.
Given that VABC is a tetrahedron where AB = AC = BC = a, VA = VB = VC = b, b>a, I have to prove that (VA x VB) x VC = ( (2(b^2) - a^2 ) / 2) AB

mint dune
fickle prairie
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Indeed, thank you.

lofty granite
fickle prairie
lofty granite
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is 19.03 correct? im not sure if i did it right

fickle prairie
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What I have so far is:
(b^2 cos(VA,VC)) VB - (b^2 cos(VB,VC)) VA

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I have to prove for vectors, but the given data is for lengths

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I don't know how to indicate vectors here

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And I have to prove this

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Sorry about the bad image quality.

lofty granite
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can someone explain how i got the answer for X as 25.45 but it says its 18 square root 2 which is literally the same answer

upper karma
#

can someone help me with this

upper karma
lofty granite
# upper karma

very appreciated. but i dont understand where the 2 square root comes from

fickle prairie
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It comes from the same theorem

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Think of it like this: a^2 + b^2 = c^2. In your case c is 10, and X takes the place of either a or b, but in this case of both, because of the 45 degree angle

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This makes it 2 * a^2 = c^2

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And now extract square root from both sides

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Now you have square root 2 * a = c

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And thus Heisenberg's answer follows

onyx knot
#

How would I solve this

wise hornet
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what have you tried

wise hornet
onyx knot
woven haven
upper karma
#

Sorry,I didn’t see you answered m8

upper karma
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this is chemistry but anyways.

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can you think of what 28% of Na, 32% of Cr and 40% of O means with respect to the mass of each component? any ideas?

storm portal
#

@fallow ruin ^^

upper karma
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Can anyone help

upper karma
#

Hey, I need help

trim breach
# upper karma

In a 45-45-90 triangle, the Pythagorean Theorem essentially is 2(a^2) = c^2.

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And since it is 45-45-90, both legs are equal length.

upper karma
#

Tysm!

lofty granite
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is anyone able to hop in a vc and help explain this math problem to me?

proven moat
#

someone help me please

trim breach
grand widget
#

What is the answer?
Can you?

tiny snow
#

Once you draw the sketch it's a very straightforward solution

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@grand widget ^

fickle prairie
#

Can someone help with university analytic geometry? I posted a problem yesterday but I'm still stuck with it

dense perch
#

For anyone looking to help laszlow, this was his question: Hey everyone! I'm stuck with an analytic geometry problem.
Given that VABC is a tetrahedron where AB = AC = BC = a, VA = VB = VC = b, b>a, I have to prove that (VA x VB) x VC = ( (2(b^2) - a^2 ) / 2) AB

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PS: I have no clue how to answer this lol. Gl

silk patio
#

Is that a cross product?

lyric quest
#

trisecting an angle with straightedge and ruler

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how do i do it for acute angles where it is possible

dark sparrow
#

straightedge and ruler?

lyric quest
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straightedge and compass

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lmao

dark sparrow
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is it even possible for any acute angles

lyric quest
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well apparently its possible for 45

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and 27

dark sparrow
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so it boils down to constructing an angle of 15 or 9 degrees respectively

lyric quest
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well thats my issue really

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is it truly a trisection to construct an angle

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because if it is, 45 degree trisection is easy

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simply impose an equilateral triangle onto it

dark sparrow
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trisection in the general case is impossible

lyric quest
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60-45=15

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but in these specific cases

dark sparrow
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so thats all you can get

lyric quest
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like i am not even using the 45 degree angle to trisect

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i am just double bisecting a 60 degree angle

feral plank
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Geometry pre test lol

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I missed a couple weeks due to a few personal reasons and my teacher wont help me setup a date after school or sometime to catch up

feral plank
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yeah lmaoo

waxen glen
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hah okay lol

feral plank
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im so stuck im trying khan academy shit dont work for me D:

waxen glen
#

do you know what is similiar triangles

feral plank
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uhh

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like what?

waxen glen
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what does similiar mean

feral plank
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yeah i know that

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kinda

waxen glen
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do you know what is "K number" in the similiar triangles

feral plank
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tbh no 😓

waxen glen
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okay lets start from what is ismiliars

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so similiar triangles' chosen side's ratios are always same

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and ratio is showen with K letter

feral plank
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yeah

waxen glen
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their height's ratios are equal to k too

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so K is ratio between similar triangles

feral plank
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ah yeah

waxen glen
#

can u say which sides are similiars in your question

waxen glen
#

wait a min let me draw

feral plank
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okay

waxen glen
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can you say that AB side and A1C1 sides are similiar?

feral plank
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so it would be

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the left and bottom?

waxen glen
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no it is not, similiarity is ratio between chosen or right sides/heights

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so AC and A1C1 are similiar

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in similiar triangles, their angles are always same

feral plank
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OHHHHH

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i got it lol that makes sense

waxen glen
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as you can see, AB side is between 90 and 30 angle

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A1C1 is between 90 and 60

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so, they cant be similar sides

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if you want to find k, just divide similiar sides/heights/medians etc

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so AB/A1B1=AC/A1C1

feral plank
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ab divided by a1b1 = ac divided by a1c1?

waxen glen
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yes, because, ab/a1b1= k which is ratio between similiar sides

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AC and A1C1 are similar sides too

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so their ratio will be equal to k

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i think i did it a bit messy lol

feral plank
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I was just making sure that the "/" was divide

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because some people write it weird

waxen glen
#

oh yes lol

#

like, why humans write ÷ ? it looks like + and actually it is a bit different than normal divide "/"

light fable
waxen glen
#

there are more difference between / and ÷

light fable
#

how so?

waxen glen
#

their solving order are a bit different

dark sparrow
#

nobody uses ÷ outside of primary school

#

also you are NOT going to pull out this 6÷2(1+2) shit

waxen glen
#

o-okay

light fable
#

@waxen glen I believe they're exactly equivalent down to how they're used

waxen glen
#

yes'nt

light fable
#

and yes, ÷ is less common in professional math contexts, but there are some times it could be preferable

dark sparrow
#

really now

#

are fractions not good enough for you

waxen glen
light fable
dark sparrow
#

then put parentheses in such a way that your expression is unambiguous.

light fable
#

you don't have to tell me

fair locust
dark sparrow
#

the whole point is that it's ambiguous as written.

fickle prairie
fickle prairie
smoky yew
#

hi, i'm pretty new here :)) i can solve this thing but it will take too long for me to type in each value. Is there any practical solution for solving this types of things?

sharp plume
#

You need to write it summation form?

smoky yew
#

there is no instruction about that but if i need to, i will... my teacher isnt that strict about methods

#

as long as the correct answer is given

#

and im still in grade 9 so i might not understand a lot of stuff :<<

silent plank
#

consider some properties of sine
sin(x) + sin(360° - x) = 0
sin(x) + sin(180° + x) = 0
and/or the locations unit circle.
you should see that there will be a lot of cancellation

smoky yew
#

thank you :)) will update later if i struggle xD

tiny snow
#

How would you go about proving that something can be inscribed in an ellipse? Five points, foci, something else?

#

Some kind of projection? A "skewed" hexagram looks like a regular hexagram seen in three dimensions from a perspective.

#

Maybe not, it can become quite elongated...

dark sparrow
#

do circles not become ellipses when seen in 3d perspective?

tiny snow
#

I think so.

#

I suppose that if I can find the projection that takes an ellipse to a circle it should take each vertex point to 60 degrees apart, and then we're done, but I am not so sure that is the simplest way.

#

That's also given that my hunch about the perspective is right.

silk patio
#

It reminds me of the reflection property of the orthocentre across a side

#

Are angle bisectors persevered under projective transformations? 🤔

#

Surely not

tiny snow
#

But I can by continuous movement of the point A transform that thing to a regular hexagram on geogebra, while all the bisectors remain bisectors.

silk patio
#

Projective transformations don’t seem to work here

tiny snow
#

No, I think trilinear coordinates may be a way forward, as mentioned here: https://en.m.wikipedia.org/wiki/Steiner_ellipse

In geometry, the Steiner ellipse of a triangle, also called the Steiner circumellipse to distinguish it from the Steiner inellipse, is the unique circumellipse (ellipse that touches the triangle at its vertices) whose center is the triangle's centroid. Named after Jakob Steiner, it is an example of a circumconic. By comparison the circumcircle ...

silk patio
#

Bashing won’t give you a vivid solution

#

This reminds me of the incircle-excircle lemma if you’ve seen that

#

I figured it out. It’s a generalisation of the 9 point circle

#

The same construction works for any point, the angle bisector condition is redundant

mighty shell
#

I understand the working out, but I keep getting the wrong answer. How do I put the right equation into my calculator? It keep giving me a totally different answer

#

That’s the answer, when I put what h equals to it’s giving my a different number

mighty shell
#

Nvm

tiny snow
silk patio
#

Yeah 9 special points are on the ellipse. Pick a point P inside the triangle. Draw the ellipse through the midpoints of AB AC and BC as well as the midpoints of AP and BP and you’ll see it passes through the midpoint of CP as well as the intersection of AP and BC, intersection of BP and AC, intersection of CP and AB

humble narwhal
#

Can anyone help me ?

#

Where tau is a translation and rho is rotation

humble narwhal
#

<@&286206848099549185>

feral plank
#

I don't understand tbh. kinda giving up at this point bc i feel stupid

waxen glen
#

@feral plank if triangle's chosen sides' ratios are same, then they are similiar

feral plank
#

I already turned it in man dont waste ur time

waxen glen
#

so, divide 10,15 or 20 with 4,6,8 and look that are they same or not

#

oh

#

ok lol

feral plank
#

second part i guess

dark sparrow
#

is this a test hmm

feral plank
#

pre test

#

the "1 point" thing is added up, like an actual test, but it goes to the hw category for our grade.

dark sparrow
#

okay

feral plank
#

I was wrong actually, it goes into the review category for my grade

dark sparrow
#

anyway

#

do you still need help with this question

#

i know it's been like half an hour

feral plank
#

yeah lol

dark sparrow
#

sorry for the delay on my end

#

ok

#

do you know what the midsegment of a triangle is

feral plank
#

yea

dark sparrow
#

okay

#

what can you tell me about the midsegment

feral plank
#

i used to be good at them but like kinda forgot the stuff bc i havent done it in so long

dark sparrow
#

bruh

feral plank
#

this is last chapters stuff

#

lmao

#

i failed the test but this should help it

#

i mean my grade anyway

#

reviews are like 30 or something %

dark sparrow
#

nice question dodge

feral plank
#

midsegment i think like

#

connects two angles?

#

or like

dark sparrow
#

no

feral plank
#

add each angle and it equals that distance?

dark sparrow
#

...

#

why did you lie to me about knowing what the midsegment is

feral plank
#

lol uh i thought thats what it was

dark sparrow
#

the midsegment connects the midpoints of two sides

feral plank
#

ah yeah that

#

i meant sides not angles whoopsie

dark sparrow
#

in any case, triangles ABC and DBE are similar, with a scale factor of 2

feral plank
#

so the answer is 2 then?

#

but how 😱

dark sparrow
#

no the answer isn't 2

#

just because i said the number 2 somewhere doesn't mean the answer to your problem is 2

feral plank
#

lol welp im dumb what can i say

#

i was kinda confused bc u said scale factor but thats not really the thing

#

the type of solving its asking

#

i mean

dark sparrow
#

one triangle is half the size of the other

feral plank
#

oh yeah lol

#

i see that now

#

LOL how the fuck did i not see that before

#

oml im special

#

yeah that makes sense

silent plank
#

is it just me or is the diagram over specified

feral plank
#

idk

#

im dumb thats why im here

#

so

dark sparrow
#

doesn't look overspecified to me

#

there's an x, a y and a z

silent plank
#

the angles don't seem the match the values of the sides given that DE is the mid seg

dark sparrow
#

why not? angle C could be 72 degrees, and angle EDB could be 63 degrees

#

and angle B = 45°

feral plank
#

so is x 45 ?

dark sparrow
#

bruh what the hell

feral plank
#

uh idk man

#

im all over

dark sparrow
#

i was not even talking to you, i was addressing ramonov's doubt about the angles

feral plank
#

ik

dark sparrow
#

how about you actually read the messages i am sending instead of plucking a number i said out of context and asking me whether that's the answer

#

4 234 45367 2342 2345623 324565344 6574536345 345345 3223453 464654562 345624579 454569 223463458 42069

#

9919299135825 32838383548 232234 01341012049 56934596394593 220342 65534

#

hymnth

#

triangle DBE is literally the same as triangle ABC but shrunk by a factor of two

#

idk what else to tell you

feral plank
#

aight

dark sparrow
#

if this isnt enoyugh for you to find the length of DE

#

then maybe you need to review similar triangles

#

instead of making me majorly upset like you just did

silent plank
#

based on the length of sides, wouldn't the angles work out to be around: ||~55.7°,~41.4°, ~82.8°||

feral plank
#

if u got upset bc im retarded ...

dark sparrow
#

there was no need to call yourself a slur

copper marten
# feral plank if u got upset bc im retarded ...

if u still need help here's the explanation:

they are similar triangles and the mid segment is DE, that means CE and EB are the same and AD and DB are the same. 5+5 is 10 which is one side of the triangle ABC and 5 is the length corresponding to 10 of triangle DEB

therefore we can divide the corresponding side lengths to get the scale factor:
10/5 = 2

since we now know the scale factor is 2, then we can find x

what is the corresponding side length to x? it's AC which is given the value of 8.
the scale factor is 2, so divide 8/2 which gives you 4

x = 4

hope that helped cat_wink

feral plank
#

thank you

copper marten
#

no prob !!

feral plank
#

it did

copper marten
#

yay :))

feral plank
#

little confusing but ill reread for the next couple to figure them out

copper marten
#

ok if you have any questions then just @ me or something lol

feral plank
#

yes i will tysm

hidden oracle
#

VECTOR

safe canyon
#

One message removed from a suspended account.

#

One message removed from a suspended account.

vapid stag
#

hey if tan x= 1/3 and tan x = sin x/cos x. This means sin x = 1 and cos x = 3 right?

silent plank
#

no

vapid stag
#

well shit

#

i just messed up my mid term question then

#

how was i suppose to tackle this if not?

silent plank
#

draw a triangle,
apply pythagorean identities

next flower
#

how would i solve for z and y. ive solved for X it is 16.2 but i dont know how to solve for z and y

vapid stag
#

well it looks like i suck at math

#

time to look for a new major?

storm portal
#

@vapid stag not necessarily

storm portal
#

i think you also have to assume that the angle made with side x and side y is a right angle

steel sage
upper karma
#

help too? lol

trim breach
# steel sage Help?

The problem gives you the range of the function, which is [4, 10], and the time span it takes to reach low tide from high tide.

#

Knowing that high tide would be 10ft, and low tide, 4ft, you should be able to produce a wave function.

covert ridge
#

Can anyone help me with this question?

copper marten
tender grail
#

am i able to ask questions for geometry here?

copper marten
tender grail
#

ok thanks

#

so basically ive been working on flow charts a bit ima send a pic of the problem

#

all ive really gotten written down is the basic parts like whats given

#

i was hoping to get some help on solving this

copper marten
#

im rlly bad at writing proofs so um .... if u dont get a response from someone then @ the helpers tag after 15 minutes

tender grail
#

ok thanks

woven haven
tender grail
#

<@&286206848099549185>

dim plaza
#

does anybody know how to

#

I need to prove that the triangle AEF is isosceles. DA and FX are parallel

#

AD is also the bisector of the angle BAC

dim plaza
#

wait I think I got it

#

I basically cut AD and FX with the transversal AC so DAC = AEF and then cut AD and FX with the transversal BF and BAD = BFX

#

no idea if it's correct though

#

should be

trim breach
tender grail
trim breach
#

Because of the givens, you can assume that RS is congruent to QT.

tender grail
#

ok i got that part so far, but i was unsure of the "official" reasoning

#

i wrote cpctc as the reason

#

is that ok or should i change that?

trim breach
#

Hm…I am not certain what you would write in the proof for that lol.

#

It’s been a while.

tender grail
#

ah no worries

trim breach
#

I think you can use CPCTC.

#

Do you know the subsequent steps?

tender grail
#

im a bit confused what you mean by that

trim breach
#

Basically do you know how to prove what you need to prove besides that step.

tender grail
#

Not really, let me grab a screen shot of what ive done so far, its really basic

#

sorry one second

#

that was my previous one

#

heres the newer one

trim breach
#

So you have proven two sides of SQR and TRQ congruent.

#

And we know triangle PRQ is isosceles.

tender grail
#

ah ok

trim breach
#

Well, you’d need to document that RQ is congruent to RQ by reflexive.

tender grail
#

ok one second

#

sorry how would i write that? would it just be rq is congruent to rq by reflexive or is it something else

trim breach
#

The actual property is called the Reflexive Property of Congruence.

tender grail
#

ok thanks

trim breach
#

So now we have two sides of them congruent.

tender grail
#

ok

#

since you know RS=QT and PS=PT would you be able to prove they are congruent from that?

trim breach
#

You need one more thing.

tender grail
#

ah ok

trim breach
#

You have two sides.

tender grail
#

PR and PQ?

trim breach
#

Yes. There is a way to prove the angles in that larger triangle are congruent.

#

Angles PRQ and PQR

tender grail
#

Im not sure of the proper way to say it but

#

woudlnt it be because it is an isosceles

#

and the bases are equal as well as the legs

trim breach
#

Yep. The Isosceles Triangle Theorem.

tender grail
#

Ok so I should add that onto the chart right?

trim breach
#

Yep!

tender grail
#

ok one second ty!

#

Ok ive added it

trim breach
#

So your next statement should be about the triangles you just proved are congruent.

tender grail
#

PRT and PQS?

trim breach
#

No.

tender grail
#

which ones would that be then?

trim breach
#

This is what you have.

tender grail
#

Yeah

trim breach
#

Those angles are in the triangles SQP and TPQ.

#

Because we only know that the largest triangle is isosceles.

#

PRQ.

tender grail
#

in the screen shot you sent there is p on the triangle twice, which one are you referencing

trim breach
#

Yeah, I just noticed that.

#

My.

#

Mb*

tender grail
#

lol all good

trim breach
#

Bottom left should be R.

tender grail
#

yeah does SQP and TPQ stay that or is it switched to SRP and TRQ

#

wait

trim breach
#

It doesn’t matter what order when you talk about triangles.

#

Only angles order matters.

tender grail
#

ok

#

I think we are good

#

it seems pretty simple from here I was kinda struggling with the begining

#

I appreciate all the help

trim breach
#

Cool. Ping me back if you get stuck or have a question.

tender grail
#

ok thanks!

tardy surge
#

Hey guys anyone able to how me with a trigonometry question ?

#

Need the area

wicked grove
tired pine
tiny snow
#

I believe this was given the necessary attention in one of the question channels earlier (cross-posted).

dark sparrow
#

alright so i got a bit of a weird question here

#

it's not that i don't know the solution, i'm just blanking on how to find it without coordinate-bashing

#

pic incoming

#

ABCD is a rectangle, BD = 7, AB = 4, show that BX = 3

upper karma
#

sick drawing

dark sparrow
#

thanks i made it in 40 seconds in ms paint

silent plank
#

similarity?

dark sparrow
#

oh yeah good point

#

EBX and EDC

upper karma
#

BX = 3

dark sparrow
#

excellent, this fills the gap in my student's 3d geometry problem.

upper karma
#

Does anyone know how to do proofs?

#

Not paragraph form. My teacher makes us do statements and reasons

willow bramble
#

@tiny snow : Is it IM that is == 5 ? or IJ ?

tiny snow
#

IM

#

IM = 5, IC = 4, KM = 4, AK = x

upper karma
#

Can anyone explain how to do this to me?

trim breach
#

Either way, if you really don’t understand it, it might be something you want to set aside a block of time to go over with someone.

near imp
#

can someone please help me on this if possible

storm portal
#

@near imp start with a diagram

near imp
#

i got everything figured out! except the function

near imp
#

can someone help me with these problems please

copper marten
#

use sohcahtoa and sum of angles

trim breach
#

Well, actually, all of the problems posted make use of trig ratios.

#

Except Question 2, which can be solved using an easy shortcut with Pythagorean Theorem.

near imp
trim breach
#

Have you Google’d the Law of Sines?

#

From the first question.

near imp
#

oh wait nevermind i got number 2

wanton phoenix
#

What about law of Sine for Q2 for Q3 since it’s a 45 45 90 there is a pattern

#

The hyp is usually the adj side with root 2

near imp
#

ok i got the answer for question 2

trim breach
#

Good.

wanton phoenix
#

Sry I meant for the last question in the order that it was given sry

near imp
#

oh don’t worry lol!

wanton phoenix
#

Yeah so for Q3 just use law of sine

near imp
#

ok i got the answer for Q3

wanton phoenix
#

Cool cool

near imp
#

and i got Q3 now i just need the first problem

rough grove
#

i need to simplify (sin x + tan x)/(1 + sec x)

#

i've tried everything I can think of, I can't simplify it

#

i know I'm just overlooking something - I really need an answer because I couldn't find anything anywhere on the internet

sweet dew
#

Can someone please give me and explanation

#

ASAP

trim breach
#

In the correct choice, the second factor does simplify to 2 with the properties of exponents.

torn tundra
#

how do i solve this? i tried it 5 times with the formula my teacher gave me and it didnt work

trim breach
#

You can set 2(mJKL) = mJL.

#

Solve for x, then the rest is straightforward.

torn tundra
#

@trim breach i did that bro

#

try doing it yourself and see if it works

#

wait

#

shit

tiny snow
#

Alright, so the problem I posted yesterday was missing two lengths, which made it have an infinite number of solutions. Here's the correct problem statement. It was supposed to be a continuation of a problem that was posted here yesterday, so it's not as well placed now as it was then.

somber coyoteBOT
tiny snow
#

I mixed up a square root... now the imaginary numbers are gone.

#

,w y^2+3^2-z^2=2^2, l=sqrt(33)+m-z-y, m^2+x^2=7^2,(l-sqrt(33)+y+z)/7 = z/3, (l-m+z+y)/7=y/2

somber coyoteBOT
tiny snow
#

So, what is the obvious solution that x = 8/3? I cannot see it...

silent plank
#

you could do it with trig and sine rule

tiny snow
#

I see how we can find <AFE, but <DHG?

silent plank
#

sine rule

#

also don't explicitly need the angles

#

just knowing the sine of the angles is sufficient

tiny snow
#

You mean this "sine rule"?

silent plank
#

dunno what that 2R on the end is supposed to represent

#

but yes

tiny snow
#

Radius of the circumcircle.

#

In order to use that you would need actual triangles, right? That have not been truncated by the square. Would you extend EF and GH to produce these, or introduce segments HE and FG?

silent plank
#

no additional construction is needed

tiny snow
#

You'll have to give me some more info then 🙂

silent plank
#

you can determine sin(<AFE) from triangle AFE
from that you can determine sin(<DHG) using the sine rule (in triangle FHP)
that would also be equal to x/7
and you can then determine x

tiny snow
#

Ah, now I see it. Ok, let me work it out.

tiny snow
#

Thanks @silent plank, that was much more straightforward.

#

Generally $x = \frac{|AE||FP|}{|HP|}$

somber coyoteBOT
#

Roenbaeck

tiny snow
#

So $\frac{|DG|}{|FP|} = \frac{|AE|}{|HP|}$ (nice ratio)

somber coyoteBOT
#

Roenbaeck

loud wolf
#

I need to calculate the TSA and V of this

#

I was wondering what do I do with the 135 degree angle, can I convert it to mm or is there a formula or formulas I can use it in to get a more accurate Area/volume

zenith copper
#

Does anybody have any idea on if you can write

#

$\frac{1}{2} ln(1 - x^2)$ in terms of inverse hyperbolic trig functions

somber coyoteBOT
#

Free Martin Shkreli

zenith copper
#

$\cosh\left(\tanh^{-1}{x} \right) = \frac{1}{\sqrt{1 - x^2}}$

somber coyoteBOT
#

Free Martin Shkreli

zenith copper
#

so

#

$\ln\left(\cosh\left(\tanh^{-1}{x} \right) = \frac{1}{\sqrt{1 - x^2}}\right) = - \frac{1}{2}\ln(1 - x^2)$

#

$\ln\left(\cosh\left(\tanh^{-1}{x} \right)\right) = - \frac{1}{2}\ln(1 - x^2)$

somber coyoteBOT
#

Free Martin Shkreli

zenith copper
#

so ln(cosh(atanh(x)) looks suspiciously like an inverse hyperb. trig function of its own to me

#

because $= -\frac{1}{2} \left( \ln(1 - x) + \ln(1 + x) \right)$

loud wolf
#

Can anyone help me...PLEASE 🥺

somber coyoteBOT
#

Free Martin Shkreli

tiny snow
zenith copper
loud wolf
#

I know I've paid a guy on fivver to make me a 3d model. But I have to show working out on area and volume

#

@zenith copper I asked already

zenith copper
#

oh, sorry

#

my bad

loud wolf
#

What do i do with 35 degree

#

135 degree*

tiny snow
loud wolf
#

It's an assignment

tiny snow
#

That's pure evil if you have to calculate it.

loud wolf
#

Part A is a worksheet- done that

Part B is a 3d model of a real life object along with calculations or TSA and volume showing working out

Part C is showing your research and putting together a report/ analysis

#

That is about 1000 words atleast

tiny snow
#

Wait, so you picked this object?

loud wolf
#

Yes becuase anything less complicated wouldn't get me an A

#

I need an A to get in advanced classes so a different school will take me becuase I've gone under a large amount of emotional abuse at this one and want to leave it behind

#

I got jumped and they gave the people a 10 minute detention. I basically go to school in the hood 😂😂

tiny snow
#

I'd ask what the least complex object that would give me A would be, while explaining the problems with the current one, then switch.

loud wolf
#

This is set in stone...

#

My teacher said I don't have to use the angle and just make it straight and use the height measurement for the width to get a about right answers but I'd have to compare to the one my 3d software gives me and explain why mine has a margin of error

#

I just want to do the angle because I want this to be perfect

tiny snow
#

Tough luck. I doubt calculations would be any more accurate than what you get from a 3d program.

#

So school pays some other person to do the modeling work?

loud wolf
#

I know my 3d program will give me 100% accuracy. But I want to get almost the exact same as the 3d model software gets to prove that I know my shit

#

I had to pay the guy...

#

Plus paid for the software, I've spent about $200

tiny snow
#

Why not do it yourself? There's free software, like SketchUp.

loud wolf
#

I've already gone too far. I also have no idea what I'm doing with 3d models

#

I've already paid the guy and brought solid works

tiny snow
#

But it sounds from the assignment that you should know 3d modeling?

loud wolf
#

It's a maths class not a 3d modelling class

#

They shrug and say "lol figure it out on your own lmao"

#

@tiny snow will you help me?

tiny snow
#

I'd split it into these parts:
A - rectangular prism minus semi-cylinder
B - triangular solid prism (x 2)
C- rectangular solid prism
D - rectangular solid prism minus 4 cylinders (x 2)
Given that I understood the drawing correctly. That'll give you simple calculations and a rough estimate.

#

If it's hollow you'd have to do some other division, but you get the idea.

loud wolf
#

Me and you had a preaty simmler idea

#

Any pointers on the other sides?

#

@tiny snow how do I find the measurements of A B C

tiny snow
#

A B C? Measurements are in the blueprint.

loud wolf
#

Well A has a length of 330.21mm but how do I find the width

tiny snow
#

What A? What are you doing?

loud wolf
#

A

tiny snow
#

Aha

loud wolf
#

For the triangles I have the hypotenuse so I just do a^2 + b^2 = c^2 right?

tiny snow
#

The blueprint is drawn to scale, so you can measure missing stuff directly and scale it appropriately.

loud wolf
#

Have to find a big peace of paper lol ight thank you for your help

dim cliff
#

can someone pls help with these two swaggy questions? thank you 🙂

finite swan
#

Sure, I'll try. Hold on a sec

finite swan
#

So for 1, you can first expand the whole thing into the base functions sin and cos: $\frac{\frac{1}{\cos^{2}x \cdot \frac{1}{\sinx}}{\frac{1}{\cos^{2}x + \frac{1}{\sin^{2}x}}}$.
Then you can simplify these into: $\frac{\frac{1}{\cos^{2}x \sinx}}{\frac{\sin^{2}x+cos^{2}x}{\sin^{2}xcos^{2}x}}$
Then you can simplify the numerator of the denominator to 1. $\frac{1}{cos^{2}sinx} \cdot \frac{cos^{2}xsin^{2}x}{1}$
If you simplify this, you will eventually get an answer of $sinx$.

somber coyoteBOT
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6EQUJ5

So for 1, you can first expand the whole thing into the base functions sin and cos: $\frac{\frac{1}{\cos^{2}x \cdot \frac{1}{\sinx}}{\frac{1}{\cos^{2}x + \frac{1}{\sin^{2}x}}}$.
Then you can simplify these into: $\frac{\frac{1}{\cos^{2}x \sinx}}{\frac{\sin^{2}x+cos^{2}x}{\sin^{2}xcos^{2}x}}$
Then you can simplify the numerator of the denominator to 1. $\frac{1}{cos^{2}sinx} \cdot \frac{cos^{2}xsin^{2}x}{1}$
If you simplify this, you will eventually get an answer of $sinx$.
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finite swan
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oof

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wait

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So for 1, you can first expand the whole thing into the base functions sin and cosine.

$\frac{\frac{1}{cos^{2}x} \cdot \frac{1}{sin x}}{\frac{1}{cos^{2}x} + \frac{1}{sin^{2}x}}$

Next, you can combine both the numerator and the denominator into one fraction.

$\frac{\frac{1}{cos^{2}x sin x}}{\frac{sin^{2}x + cos^2{x}}{cos^{2}x sin^{2}x}}$

Then you can multiply the reciprocal of the denominator times the numerator.
$\frac{1}{cos^{2}x sin x} \cdot \frac{cos^{2}x sin^{2}x}{1}$

Finally, you can simplify and eventually get the final answer of $sinx$.

foggy perch
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For 2 you can rearrange it to get $(\sin x )^2=1/2$ so then you have two equations, $\sin x=\sqrt{2}/2$ and $\sin x=-\sqrt{2}/2$. Find the values of x in the asked interval for each, then combine both lists

somber coyoteBOT
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6EQUJ5

dim cliff
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thank you guys! for number two tho mikey, i don’t really know how to do the interval thing could you help with that as well

foggy perch
silk glade
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Can someone please help me with this question

earnest echo
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You can find the height of the given right triangle

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And after that use Pythagorean theorem

vestal pendant
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@earnest echo and to find the height i'd need to do 40/tan 45, or do i use special right triangles

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our teacher is out on leave and we have no one to teach us this unit, we were basically on our own

earnest echo
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Use the area

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And where are you getting tan45???

vestal pendant
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45-45-90 triangle

vestal pendant
earnest echo
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How do you know that?

vestal pendant
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true

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we arent given a second angle measure

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so it could literally be 90 44 and 46 for example, so i shouldnt use that

earnest echo
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Yeah

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Use the area

vestal pendant
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alright

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@earnest echo Thanks. I was able to solve it.

earnest echo
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👍

vestal pendant
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@upper karma Already solved, and they arent looking fo simplest radical form

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"to the nearest tenth of a meter"

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Thanks though ❤️

upper karma
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Oh, I missed that detail sorry bud ❤️

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Does anyone know how to factor equations

humble pulsar
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next time just ask your question

upper karma
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Yeah

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so do you?

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I need help in this question

finite swan
inland mountain
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Whats the equation in order to get cos x?

silent plank
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pythag

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to get the 3rd side

inland mountain
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Ok thank you

finite swan
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After you get the 3rd side, remember cosx = adjacent side / hypotenuse

inland mountain
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Yea I did cos-1(12/20) and got 53.13

finite swan
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Nope

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You got the right side length

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The adjacent side is 12. The hyponetuse is 20. Therefore, cosx =?

inland mountain
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Uhm

finite swan
silent plank
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the question doesn't ask you to find x, nor do you need to

finite swan
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Yup

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You solved for x

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The question asks for cosx

inland mountain
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Oh so the answer is just 12/20

finite swan
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Yup

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But you can simplify

inland mountain
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Oh thats why I was confused

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So if I have to find the measurement of c would I use tan?

obtuse tapir
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yes

obtuse tapir
silent plank
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wdym

inland mountain
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It would be 1 right?

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Im just checking

storm portal
inland mountain
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Steve is standing on a hill and his line of sight is 51 feet directly above the ground. He can see two deer grazing in the distance. If the angles of depression to the deer are 35° and 47° how far apart are the deer?

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Okay so this is my homework question and I dont know how to even send up the triangle to this question

trim breach
inland mountain
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I tried it doesnt look right

trim breach
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Just a sec.

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Handwriting is bad and small lol.

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But it should look like this.