geometry-and-trigonometry

[upper karma]

nvr mind.. I got it!

[obsidian harness]

Oh nice

[gentle ibex]

The volume of a cube is 216 in squared find the length of an edge of the cube and the surface area of the cube

[trail tendon]

you need help or ?

[gentle ibex]

Some guy answered it in chat

Idk how he did it so fast though

[trail tendon]

the formula for a volume of a cube is x^3, where x is the length of the edge

so x^3 = 216, x = cbrt(216), which is the length of the edge

and then you just square the length and multiply by 6 to get the surface area

[gentle ibex]

@trail tendon

[astral shadow]

What is the Sa

Its saying what I inputted was wrong but I thought it was 4799.3

[zealous olive]

should be 2 times the SA of all the visible sides as well as the SA of the bottom rectangle

you must've counted the bottom rectangle twice

[zealous olive]

also you calculated the area of the triangle wrong

[coral needle]

I need assistance with geometry

[exotic yarrow]

Direct application of the angle bisector theorem

Look it up if you don’t know

[drowsy glade]

Someone who can help me with a free time for study for my exam?

[lime dune]

!da2a

[lime crown]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[maiden brook]

what’s it on?

[graceful maple]

Hey yo

[echo beacon]

4am someone sauce a question

need to cook up

[obsidian harness]

Let $ABC$ be an acute triangle with altitude $AD, BE, CF$, orthocenter $H$. Let $P$ be the orthogonal projection of $D$ on $EF$. Prove that $PD$ is the internal bisector of $\widehat{BPC}$.

[somber coyote]

south

[obsidian harness]

if you haven't learned this yet you should ask for a more specific kind of question

[faint pasture]

Is the last line to the solution "hence proved"?

[obsidian harness]

no

[echo beacon]

what the flip

give a

gr 10 problem

i’m on no sleep

[obsidian harness]

trig?

I won't post anything as evil as that, dw

[echo beacon]

anything

just

NOT PROOFS

😭

[faint pasture]

Sad

I thought i had it

[obsidian harness]

source: ||https://math.stackexchange.com/questions/4922250/a-geometry-problem-involving-three-altitudes-of-a-triangle||

[strong seal]

Hey does anyone now to find an angle (0, 360) between 2 vectors?

[obsidian harness]

here you go

[echo beacon]

that’s just something from a test i get

gimme sometjignharder

like

lemme give an example

[obsidian harness]

yes, try using the cosine rule

[echo beacon]

question 26

[strong seal]

it does give anything over 180 tho

[echo beacon]

gimme something along that difficulty

[obsidian harness]

If you want the reflex angle, just do 360 - your angle

[obsidian harness]

https://cemc.uwaterloo.ca/contests/past_contests.html

you can try looking for a geometry question in there

[echo beacon]

NOOOO CANCERRRR

I ALWAYS

SCREW UP

ON THE CONTESTS

Kvkejdjcjjdnfhfhff

i’m gonna jump bye guys

[strong seal]

but like in this example how can i differentiate between AC and AD?

it'll just give me the same angle no for AC and AD

[obsidian harness]

45 degrees is the angle between AB and AC

45 degrees is also the angle between AD and AB

So if you want the reflex angle, you need to do 360 - 45 = 315

[strong seal]

but i what if i always want the clockwise angle no matter if it's reflex or not

[obsidian harness]

you should draw it out like you did on Geogebra but you could also try on paper

so that you can figure whether you need to do 360 - x or not

[strong seal]

it's okay i found the solution

thank you tho

[obsidian harness]

no worries

[sand patrol]

Can anyone help me how to find the area in colored part

[lime dune]

is that supposed to be a circular arc

if not then i don't think there's enough information

[sand patrol]

Rly

[lime dune]

bc the answer is gonna be

[area of trapezoid] minus [area of that circular/elliptical/??? region]

for both of those you need to know the height of the trapezoid

[sand patrol]

Idk the question just says find the area In the colored part

[lime dune]

are the other questions around it

all involving circles?

[sand patrol]

Yea

[lime dune]

so maybe we can just assume it's a circle hmm

ok so in that case

what's the height of the trapezoid?

[sand patrol]

It’s not given

[lime dune]

if we assume the non shaded region is a semicircle

then we know what the height is

what is it equal to?

(don't overthink it)

||the radius of the semicircle, 7||

[sand patrol]

So the radius is the height

[lime dune]

that should be enough info to solve the problem

[sand patrol]

K Tnx

[lime dune]

^

np

[sand patrol]

Any help find the area of the a colored area

[grave pond]

Can you find the area one of the two parts?

[obsidian harness]

!nosols

[lime crown]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[obsidian harness]

oh fair

[sand patrol]

Isn’t area of the full circle is pi*r^2

[obsidian harness]

exactly

[sand patrol]

So area of semicircle is 1/2pir^2

Tnx

[hoary totem]

if the height of the trapezoid is h, the area is
trapezoid area - half-ellipse area
((20 + 7) * h)/2 - 7 * h * pi / 2
(27 h - 7 h pi)/2

[lofty spear]

what might this be?

certainly, it doesn't belong to this channel

is this just a list of topics in math?

what do you want to do with that?

[fleet aspen]

i have the EVAU test on wednesday next week and im struggling to understand analytical geometry on space anyone who can give me a hand ?

[stuck sleet]

It cannot be negative?

[visual bison]

Sure. But it’s it equal to another positive angle.

Like -pi/2 = 3pi/2

[stuck sleet]

ok thanks

[sinful heath]

having trouble with compass bearings trigonometry is starting to get to me 😭

[grave pond]

Have you drawn a diagram?

You're not supposed to keep that kind of situation in your head.

[sacred nimbus]

is the distance formula needed to solve for this question?

[grave pond]

No.

You can wither write down equations for each of the diagonals, and solve to find their intersections.
Or: since you're being promised that it's a parallelogram, you can use that the diagonals in a parallelogram cross each other exactly halfway through each diagonal.

[formal geyser]

Can anyone help me to find the blue area

I already found the blue area plus the small circle inside of it

I don't know how to find the area of the small circle

[grave pond]

Figure out its radius first.

[formal geyser]

Of the small one?

I dont know how

[grave pond]

Yes.

[formal geyser]

Can you give me a hint

[grave pond]

The sum of the two red lines is 10 cm.

And the triangle is 45°-45°-90°.

[formal geyser]

To be honest i dont know what to do next

Moreover, i dont understand why this triangle is 45°-45°-90°

[grave pond]

I hoped it would be obvious that the line that connects the centers of the two circles points towards the corner of the square and must therefore be at an angle of 45°.

[formal geyser]

I understand it now

[grave pond]

So the next step is to write down an equation that the radius of the small circle must satisfy.

The step after that will be solving that equation.

[formal geyser]

r is 0.86?

my equation is r + 5 = (5 - r)*sqrt(2)

[grave pond]

I've no idea.

That equation looks reasonable. If it gives you 0.86, then go with that.

[formal geyser]

Okay, thanks

Thank you a lot

I solved the whole question correctly and found blue area

[past solstice]

For my test I gotta know these graphs, do I have to learn them or is there a way during the test I can make these?

Do I just have to learn what a cot,cosec and sec graph look like

[faint pasture]

<@&268886789983436800>

[trail tendon]

pretty much u just gotta know what thye look like...

[grave pond]

Keep that to #chill, please.

[past solstice]

My bad i didn’t know it was gonna be so big it was an emoji on my keyboard

[past solstice]

Damn the cot,cosec and sec ones so complicated:(

[cunning lion]

if you know what the sin, cos graphs look like then it follows from that

[trail tendon]

a.k.a it flips, but also since a function cannot have multiple y values for one x value it has a range restriction

depending on which graph

[past solstice]

🧐

[trail tendon]

ignore what i said i was thinking of inverse trig functions

💀

these dont flip nvm

[jagged wyvern]

Can someone help me with this?

Am I suppose to find each midpoint of each of the lines that can be formed

Because I end up getting decimals which i cant graph

They only let me graph whole numbers

[lime dune]

you’re given the midpoints

ie the vertices of the midsegment triangle

[jagged wyvern]

I gotta graph 2 triangles

[lime dune]

hint: using the midpoints, you can find the vertices of the original triangle - set up some equations to solve for their coordinates

[valid gull]

what should I learn of Algebra, so I can move on to trig?

[lime dune]

don’t see it as a means to an end, learn it thoroughly

at a bare bare minimum, you should be comfortable with solving linear and quadratic equations in one variable, and working with exponents and stuff

[trail tendon]

cuz after trig and maybe even during trig theres still algebra ._.

especially after ._.

[gentle haven]

One thing I can think of is the coordinate plane maybe. I think the unit circle relies on that.

[valid gull]

I am so sorry. I mean what can I learn of Geometry not Algebra LOL.

Basically I know nothing about geometry other than the basic shapes. Absolutely nothing. Right now I'm re(learning) basic arithmetic, then I'll move on to Algebra 1 and 2, and will have to move on to Trigonometry. However, geometry is missing along the way and I don't know what can I teach myself

[valid gull]

@trail tendon @gentle haven

[valid gull]

Coordinate plane is mega important. I definitely do not remember if X and Y is up horizontal or vertical so thats a must

Anything else?

[trail tendon]

x is horizontal, y is vertical

[trail tendon]

uhh

[valid gull]

right i know that but i gotta remember that

but ill prob remember after your reply

[trail tendon]

for geometry i would learn angle manipulations and maybe areas of 2d shapes

[gentle haven]

Things related to triangles maybe

[trail tendon]

oh yeh definitely

[gentle haven]

Pythagorean theorem, etc.

Lots of theorems

[valid gull]

Right thats super important

[trail tendon]

what other theorems?

[valid gull]

angles, areas of 2d shapes including triangles

[gentle haven]

Sas, asa, aas

[trail tendon]

what else?

[valid gull]

what

[trail tendon]

i don't have strong geometry 💀

but i know those at least

[valid gull]

how strong does ur geometry have to be to learn trig, and to learn calc?

[trail tendon]

well im learning calc, and i know trig, and my geometry is mid

lol

[gentle haven]

Congruence theorems

[valid gull]

i mean i've seen all of that throughout my schooling but unfortunately i never studied :/

[trail tendon]

maybe i know geometry better than i think but

still its like

._.

[valid gull]

so having outstanding algebra skills is better than having outstanding geometry skills?

idk

[trail tendon]

definitely

[valid gull]

got it

[valid gull]

right

[trail tendon]

i would know like formulas to calculate circle, triangle, trapezoid

[gentle haven]

I think there's more alg than geometry in trig

[trail tendon]

rectangles ofc

[gentle haven]

Apart from triangles and circles

[trail tendon]

i would actually argue the opposite?

[gentle haven]

How so

[valid gull]

those r the shapes u see the most in calc?

or calc has no specific shape

[trail tendon]

i mean at least the trig functions are based on triangles from the unit circle

[valid gull]

deefinitely

definitely

[valid gull]

😭

[gentle haven]

Yeah but apart from that what else geometry is there

[trail tendon]

in calc, you might use these to calculate harder shapes, more or less. also, you get to derive the formula for area of circle 💀

kind of 💀

[trail tendon]

what algebra is there?

[valid gull]

interesting

[trail tendon]

i mean

i guess the trig identities technically

but the basic ideas of trig functions are more graphs and unit circle

and angles

[valid gull]

so
Area perimeter and volume of 2D shape
Area perimeter and volume of triangles
Pytagorean theorem
SAS, ASA, AAS (Congruence theorems)
formulas to calculate circle, triangle, trapezoid, rectangles

all of those r part of geometry?

or trig

[gentle haven]

Ratios, linear equations

Uh

[trail tendon]

you can't have volume of 2d shape, but yea

[trail tendon]

in trig? where?

[gentle haven]

Variables

[valid gull]

right

thanks

[trail tendon]

i guess 💀

[valid gull]

r 3d shapes trig or geometry?

[gentle haven]

Sin cos, etc. those are ratios right

[trail tendon]

geometry

[gentle haven]

Tangent gives a slope

[valid gull]

tan

[gentle haven]

Shocking

[trail tendon]

thats not algebra, thats...division...

[trail tendon]

i mean idk if variables are only algebra, and everything with a variable is algebra

lol

i dont know how its classified

[gentle haven]

Algebra deals primarily with variables right

[valid gull]

yess

[trail tendon]

sure

ok

i guess practically every math subject is algebra then, to an extent 💀

[gentle haven]

Sinx=o/h
I feel like that would be algebra

[gentle haven]

Yeah

[valid gull]

sort of yea

you're so right

[gentle haven]

It's always been algebra

[valid gull]

so circles, triangles and rectangles r the most commonly used shapes?

is that it

[trail tendon]

calc 1 is just algebra 3, lets be honest

[gentle haven]

Fr

[trail tendon]

calc 2 is algebra 4 🗿

[gentle haven]

I suppose so

[valid gull]

and so on and so forth

[trail tendon]

calc 3 is maybe geometry 2 😂

[valid gull]

HAHAHAHA

[gentle haven]

Geometry is algebra 1.5

[valid gull]

@trail tendon which calc r u learning rn

[trail tendon]

2

[valid gull]

wow

is it super hard

compared to 1

[trail tendon]

i havent gotten that far, but i wouldnt say its too much harder 💀

yet, at least

💀

[valid gull]

lets say i take calc 1 in the fall of some random semester, and then i have a 1 month break to spring semester

and spring semester is calc 2

can i self study a bit

of calc 2

so i get an A

?

or is it super hard and barely anyone gets an A

[trail tendon]

oh u probably could get an A

its not that much harder than calc 1

if you got an A in calc 1, u can prolly get an A in calc 2

[valid gull]

right

everyone says it so hard for no reason

[trail tendon]

at least, i hope 💀

[trail tendon]

its hard if you look at it without context and have no idea whats going on, i guess 💀

[valid gull]

i'll take precalc 1 this fall, precalc 2 next spring

then calc 1 then calc 2

[trail tendon]

it may depend on the teacher, the teacher could give really hard problems

mine didnt

[valid gull]

i can def prepare a lot in the summer so i learn calc 1

fall of 25

[valid gull]

i hope not

[trail tendon]

💀

[valid gull]

@trail tendon if i study a lot these 2 chapters before my fall semester where i'll learn precalc 1 do u think ill be prepared

although they wont use this book, they'll cover chapters 1-4

so ideally i'd learn the first 2 chapters

[trail tendon]

those are really important, it may not be all you need to know but i can't really think of anything else off the top of my head so that would be great to study that, you'd be in a good place at least 😂

[valid gull]

ye def not all they cover more

[valid gull]

exactly thats my goal thanks

[brisk adder]

Converting polar coord. to rect. coord.
Hi, can anyone help me out here? Idk what did i do wrong, i already make sure i use in radian, but still getting the slightly different answer from the video.(-4.75,-3.67) Did i miss anything, or did the lecturer make a mistake there?

(sry i sent wrong pic)

,calc 6cos(3.8 rad)

[somber coyote]

Result:

-4.7458062714865

[brisk adder]

,calc 6sin(3.8 rad)

[somber coyote]

Result:

-3.6711473456563

[valid gull]

@trail tendon @gentle haven thank you so much you guys are awesome. Lots of love from Mars

[trail tendon]

dude you live on mars???

[valid gull]

i was born in mars!

rn im living on mars yes

[trail tendon]

i got the same thing he got, idk how u got that

did you use degrees but put the answer in radians?

[brisk adder]

^ i use radian mode then typed 6cos(3.8)

[brisk adder]

hence this answer

[trail tendon]

um

182 degrees is about 3.17 radians

[brisk adder]

can you show me how u doen it with teXit

[trail tendon]

i dont know texit

also uh

6cos(3.8 rad)?

it should be -3.1cos(182 deg) or -3.1cos(3.17 rad) if you really want to round

[brisk adder]

thats werid, i converted it to degree and it does give the correct answer

but idk where i did wrong with rad

[trail tendon]

i think its the 6

instead of -3.1

lol

[brisk adder]

eh

,calc -3.1cos(3.8 rad)

[somber coyote]

Result:

2.4519999069347

[brisk adder]

now im confused

so why are we converting polar coord again

[trail tendon]

they're converting polar to rectangular... for teaching purposes 😂

[trail tendon]

it should be more like 3.17 rad, not 3.8 rad

[brisk adder]

cant we just plug them in the formula, x=r* scos theta and y=r* sin theta

[trail tendon]

yyes

thats what you're doing

oh i see

[trail tendon]

thats from rectangular to polar

actually no

its from polar to rectangular

mb

lol

[brisk adder]

i think my problem here is understand why cant i just plug in 3.8 rad, and where did 3.17rad come from.. From previous example, ive only been plugging in only, i dont really need to worry about converting..

[obsidian harness]

Pi rad = 180 deg

So 182 deg = 182/180 × pi rad

,calc 182/180 * pi

[somber coyote]

Result:

3.1764992386297

[obsidian harness]

Mhm

[obsidian harness]

You need to convert to radians first

Then you can just plug in

[brisk adder]

but isnt 3.8 rad. in radian already?

[grave pond]

Where do you get 3.8 from in the first place?

It's not anywhere in the picture you posted.

[brisk adder]

is the question

and we are asked to convert it in rect coord

[obsidian harness]

Ah 2 different questions got it

[grave pond]

Huh, that looks completely different from what you posted first.

[brisk adder]

oh lol, mb i think i sent the wrong pic

should be this

[grave pond]

My calculator agrees with yours.

Any particular reason not to think the person in the image made a mistake?

[brisk adder]

hmm, i guess they made an error? I did see comment about people getting the different answer, but no one is knowledgable enoough to be able to confirm it

https://youtu.be/nyab0CZK2BE?t=1852

here is timestamp

[grave pond]

Their angle seems to be right, but srqt(4.98²+3.85²) is 6.29 rather than 6.

[grave pond]

The video simply jump-cuts to having wrong numbers on the whiteboard, no hint of how they came about.

[trail tendon]

prolly cuz he put it in a calculator, remembered the wrong number or smthn 💀

[brisk adder]

^

[brisk adder]

welp, so can we agree (-4.75,-3.67) is the correct answer?

[grave pond]

Yes.

[brisk adder]

sorry about the confusion earlier btw, do you get the same answer like this?

[trail tendon]

yes

[brisk adder]

case close then. Thanks guys

[icy loom]

don't know if this is the right place to ask but

i know you can project from $\mathbb{R}^n$ to $\mathbb{R}^m$ such that m < n (usually), but i want to know if there's a term for a specific kind of action from $\mathbb{R}^n$ to $\mathbb{R}^{n+1}$ where you have some shape and you "lift it up" to form a shape of the dimension one above

[somber coyote]

haru~

[icy loom]

https://upload.wikimedia.org/wikipedia/commons/d/d9/From_Point_to_Tesseract_(Looped_Version).gif

as in this

or less generally the action of taking a 2d shape and making a prism with it

[stuck sleet]

My answer is 9 pegs, but the right one is 10 pegs

My solution is that the 4ft board = 48 inches

minus the ends which is 2*6 = 12 ; therefore 48 - 12 = 36

then 4 inch spacing per peg so 36/4 = 9

What did I do wrong is my picture wrong?

[stuck sleet]

this is my picture

the distances between pegs

Is my picture wrong?

[lime dune]

what you’ve drawn adds up to 44 in

how many inches are in 4 ft?

[stuck sleet]

48

[lime dune]

so we can add in one more peg

be careful of these “off by one” errors

they’re quite easy to make on questions like this

[stuck sleet]

Thanks bro

yeah I got the drawing wrong

confusion

[lime dune]

npnp

[upbeat charm]

Hey. I was wondering if anybody could give me some suggestions for online resources that I could use to get started learning geometry

[lime dune]

anything pre university is generally covered passably by khan academy

it’s not great, it just .. gets the job done

[upbeat charm]

alr thx

[stuck sleet]

try the book by moise and downs (Geometry, Metric Edition)

or

You can also try what am I reading now by Alexander (Elementary Geometry for College Students)

[upbeat charm]

those look pretty interesting. thx!

[brazen cloak]

https://youtu.be/qW6Ua50fTw8?t=399
over here how is he breaking the tangent into two diff angles??

[hoary totem]

observe that 15pi/6 is 12pi/6 + 3pi/6
and 12pi/6 has no effect on the angle because its just 2 pi, its just a full revolution around the circle

so 15pi/6 is the same angle as 3pi/6

which simplifies to pi/2

[worldly rivet]

Can someone please help me? #help-14

[brazen cloak]

so he broke it up into 2pi and the remaining angle??

right?

[wise nest]

can anyone help? im rly struggling i need all the help i can get and i havent found any

plz i REALLY need help i will fail if i dont get help

nothing has helped

this is my last hope and no one has answered my forum'

[gentle haven]

What do you need though

[faint pasture]

https://dontasktoask.com

[wise nest]

like theres various topics beause my teacher doesnt know how to teach

[gentle haven]

Like what

[wise nest]

area of a regualr polygon thats one

[kindred granite]

guys

can anyone help with proof of area of circle?

[trail tendon]

which proof?

integral proof?

[kindred granite]

ya

[trail tendon]

can't you just do trig sub?

like uh

the equation of a line is y^2 + x^2 = r^2

obviously you can't integrate that with respect to x or y

[kindred granite]

k

[trail tendon]

but y = +- sqrt(r^2-x^2), right?

[kindred granite]

yeah

[kind cloak]

Oh damn, I’m taking this shit next year

[trail tendon]

and since the area of +sqrt(r^2-x^2) is the same as -sqrt(r^2-x^2), you can just integrate +sqrt(r^2-x^2) and multiply by 2?

[trail tendon]

this aint really geometry either lol

this is more calculus 💀

but it kind of

geometry relateed

[kindred granite]

yeah so far so good

[trail tendon]

alr and the bounds are -pi to pi, right?

because those are the ends of the circle?

[kindred granite]

yup it is

[trail tendon]

so now you have sqrt(r^2-x^2)

just realized

mb

i was taking unit circle

im gonna change the 1 to r^2 lol

[kindred granite]

kk

[trail tendon]

alr

so you have uh

[kindred granite]

OOO I JUST WATCHED VID AND FOUND OUT

KK THX FOR HELP ANYWAYS

[trail tendon]

oh alr nice

[hoary totem]

here is the derivation of the formula for the area of a regular polygon

observe that any regular n-gon can be split up into n congruent isosceles triangles (5 triangles shown for the pentagon)
so we just need to find the area of 1 triangle and multiply by the number of sides

also, the sum of all exterior angles is 360 degrees
since this polygon is regular, one exterior angle (red angle) is 360/n degrees
that means 1 interior angle is 180 - 360/n degrees (blue angle)
so the angle of one of those triangles (green angle) is half of blue so (180 - 360/n)/2 = 90 - 180/n degrees

now, say the side length of this polygon is s
now we have that the purple length is s/2
and also, since tan(x) = opposite/adjacent, we have red length = tan(green angle) * purple length
or red length = tan(90 - 180/n) * s/2
red length is the height of one of those triangles, and the area of a triangle is bh/2
so the area of one of those triangles is (s * tan(90 - 180/n) * s/2) / 2
or s^2 tan(90 - 180/n) / 4
or s^2 cot(180/n) / 4

now we just multiply by the number of sides because there is 1 triangle per side
so we end up with:
area of whole regular polygon = n s^2 cot(180/n) / 4

[north kindle]

I’m having some trouble with this problem, the books hint says to try and find the area of PXQ divided by the area of ABC, but since I don’t know anything about the altitude I’m trying to prove PXQ and UAR congruent but I’m finding myself unable to do so.

I’m not sure I’m going down the right path but I’m not sure how else to go about this

Wait no they can’t be congruent

[nocturne remnant]

they are similar, but (generally) not congruent

[north kindle]

Hmmmm

I’m not sure how to find [PXQ]/[ABC] in terms of PQ and BC without knowing anything about the altitude

[nocturne remnant]

honestly idk what the hinted approach is, seems like you can do it without using any areas

[north kindle]

My idea is to use area to find the scaling factor between triangles and then doing something with that

And that seems to be what the books hinted approach is

But I do not know how to actually do that

[nocturne remnant]

can you relate, say, RS/CA to some other ratios using similar triangles?

[north kindle]

Well it equals RX/BC and SX/AB

But I don’t see how that helps

[nocturne remnant]

if you use RX/BC

and convert the other one to .../BC as well

all three denominators become BC

[north kindle]

What other one

[nocturne remnant]

TU/AB

[north kindle]

Oooooh

That could do something maybe

[nocturne remnant]

PQ/BC + RS/CA + TU/AB = PQ/BC + RX/BC + UX/BC

after that youre pretty close to the solution

[north kindle]

So we need to show PQ+RX+UX = BC

Which I think we can do fairly easily

By just showing RX = QC and UX = BP

I’m not sure if that’s trivial or not

[balmy skiff]

Anyone know how to do scale factor

[nocturne remnant]

it is quite trivial

[tropic flame]

<@&286206848099549185>

<@&286206848099549185>

[lethal peak]

dont spam

[tropic flame]

Sorry

Mb

Where r the helpers

[glass sparrow]

!help

[lime crown]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[nocturne remnant]

@tropic flame please post your question before tagging/asking for help

[tropic flame]

Yep

Done

[tropic flame]

Alr mb I'm new here

[nocturne remnant]

!status

[lime crown]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[nocturne remnant]

and do you need help on both 10 and 13

[tropic flame]

Yh

[nocturne remnant]

!status

[lime crown]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[tropic flame]

1 buddy

[nocturne remnant]

ok

have u heard of pythagorean theorem

[tropic flame]

Pythagoras

Yh

[nocturne remnant]

for question 10, you first need to find the (horizontal) distance between lines AB and CD

which is equal to distance AD

[tropic flame]

Alr

[nocturne remnant]

do you know how to do it?

[tropic flame]

No

[nocturne remnant]

hmm

[tropic flame]

👨🏿‍🦲

[nocturne remnant]

uhh you want to use the 13cm in some way

so

[tropic flame]

Alr

[nocturne remnant]

drop the altitude from B to CD

call that point E

[tropic flame]

Oo

Ok

[nocturne remnant]

like this

[tropic flame]

Ooooooooooooooooooh yh I knew it

[nocturne remnant]

notice that BADE is a rectangle

[tropic flame]

Yep

[nocturne remnant]

so can you find the length of CE?

[tropic flame]

4

[nocturne remnant]

what

no bro

[tropic flame]

What

[nocturne remnant]

how did you get 4 💀

[tropic flame]

Bro I'm trash at geometry

[nocturne remnant]

answer my question how tf u got 4

[tropic flame]

I halfed 8

[nocturne remnant]

bruh

it's not given (and in this case not true) that E is the midpoint of CD

so dont assume that

💀

anyway

[tropic flame]

9k

Ok

[nocturne remnant]

since ED = BA = 3cm, CE will be 8 - 3 = 5 cm

[tropic flame]

Oooh yep

[nocturne remnant]

ok so now apply pythag thm to find BE

[tropic flame]

I don't get it bro

Send me a pic

[nocturne remnant]

you already have BC and CE

and a right triangle BCE

and i am asking for BE

[tropic flame]

Show me how u solve it in a pic and I'll get ikt

[nocturne remnant]

i dont think it makes any difference

[tropic flame]

It does

I understand faster

[nocturne remnant]

do you actually know pythag thm

[tropic flame]

Yh

Gimme a questions

[nocturne remnant]

can you just state the theorem rn

[tropic flame]

No

[nocturne remnant]

if you know it you should at least be able to do that

[tropic flame]

Gimme a question and I'll do it

[nocturne remnant]

the question is right in front of you

BC = 13 cm, CE = 5 cm, and BEC is right angle, and you need to find BE

[tropic flame]

Ok

[nocturne remnant]

can you do that?

[tropic flame]

Lemme see

Gimme 2 mins

13

Buddy

[nocturne remnant]

??

[tropic flame]

Is it wrong

[nocturne remnant]

yeah

[tropic flame]

👨🏿‍🦲👨🏿‍🦲

[nocturne remnant]

BC = 13 is the longest side, how you gonna have BE = 13 too

[stray elbow]

can I post my question here?

[tropic flame]

That what I said

13

I'm right innit

[nocturne remnant]

if its related to geometry or trigonometry then yes

[nocturne remnant]

wdym

bro

BE

[tropic flame]

U asked for BE

[nocturne remnant]

yes

[tropic flame]

BE=13

[nocturne remnant]

can you show your working

[tropic flame]

Nvm

[nocturne remnant]

?

[tropic flame]

Mb

Bro

Continue

[nocturne remnant]

what's your answer

[tropic flame]

Idk

[nocturne remnant]

so you cant do it after all

🗿

[tropic flame]

U know what

Imma call ma boi maths genie

[nocturne remnant]

so do you still need help

[tropic flame]

Nah its ok

Imma move on to trigonometry

Alr

Thankk

Thanks

[nocturne remnant]

💀 ok

[tropic flame]

Cya

👨🏿‍🦲

[nocturne remnant]

@stray elbow did you have a question?

[grave pond]

(If he does, he can't post it).

[nocturne remnant]

damn

average maths server encounter

💀

[grave pond]

Evidence suggests it would probably have been 2+2.

[autumn pelican]

How does theta equal that? THe formula I was given was tan0 = y/x, 0 = arctan y/x which equals -45

[cunning lion]

they ask for 0 < theta < 2pi

so it needs to be in radians, and in that particular range

[autumn pelican]

Oh.. you're right, thank you

Actually I seemed to only be able to get that to work for one question

This is in radians, and within the range

Oh, nevermind it was +2pi'd

[long trout]

im in 8th grade

but not in usa so the studies are different

its d?

[trail tendon]

"and intersect AC in D..."
what intersects there?

💀

[long trout]

i think the opposite

[trail tendon]

the opposite what?

[long trout]

I think they mean d intersects at ac

like its a part of it

[trail tendon]

BD intersects AC at D i think its saying

[long trout]

yeah

whats the answer?

[trail tendon]

i don't know what {D} or {A} means lol

or projection 💀

[long trout]

did u take these before in ur life

?

[long trout]

point a or point d

[trail tendon]

take what?

[long trout]

projection lesson

[trail tendon]

i guess not?

how did you get {A}

[long trout]

its choose

[trail tendon]

how did you get it though

[long trout]

i never said a

?

i said d

[trail tendon]

oh i thought you meant choice d

[long trout]

nahh

[trail tendon]

how did you get {D}

[long trout]

is it wrong?

[trail tendon]

i don't think so

I don't know exactly how you got it though

were you just guessing because its the point of intersection? 💀

oh wait

[long trout]

i dont know how to explain it

[trail tendon]

im dumb

[long trout]

since i take it in arabic

[trail tendon]

ahh

[long trout]

i also have another one but its about the same damn lesson but i dont know the answer

[trail tendon]

no actually i think it is {D} because both BD and AC intersect the point, so technically the line is just...rotated about the point {D}

i don't know for sure though

[long trout]

another one

i dont know this one

[trail tendon]

i think someone who actually knows this should uh

💀

[long trout]

lmao

i think its either c or d

But im not sure

[trail tendon]

how did you get those?

[long trout]

in my book theres a rule that when they are parallel the projection equals the origin (bd) so bd =8 and so does its projection but when its a normal not parallel the origin is always bigger than the projection

unless they typed the question wrong cuz im losing my mind

if they mean its still parallel for the rest of the question it equals 8

[trail tendon]

what does // mean 💀

[long trout]

parallel

[trail tendon]

oh

wouldn't the length of the projection be 8?

oh

[long trout]

yeah thats what i said

[trail tendon]

im reading ur reasoning again hold on

i mean if projection means you map BD on AC

i would think the length of the "projection" would be 8

the same length as BD

unless im trippin

[long trout]

yes

thats what im saying fr

[long trout]

yeah u map it draw two points from both ends of bd so b and d on ac which is the straight line

so they r called b dash and d dash

[trail tendon]

B' and D'?

[hexed tusk]

pretty sure its 8

[long trout]

yes

[trail tendon]

did ur teacher call them dash?

or r u self studying, or are they really called dash

lol

usually id think they were called prime

B prime -> B'

mebe not tho idk

[long trout]

they called dash

for me

[trail tendon]

weird

[empty quartz]

i need hella help

[trail tendon]

nice

[empty quartz]

shit should be easy but im secon guessing

geometry has been so easy til now for me

its just so weird

i need som1 ina call to help me stgggg

[trail tendon]

you know how to calculate the surface area?

[empty quartz]

yea TSA+2b+LSA

lateral surface area + 2b (b=base)

[trail tendon]

it doesnt want lateral surface area

just regular

[empty quartz]

and the whole pythagoran therom i think idk bruh

so would i do the box technique

lemme show

[trail tendon]

alr

[empty quartz]

this is some she did that i checked and got right

[trail tendon]

yeah

so in order to calculate the area of the rectangle, you need that last side of the triangle

since it tells you its a right triangle, you can use the pythagorean theorem

[trail tendon]

so how do you apply that here

[empty quartz]

24^2+b^2=25^2

idk tbh, i think thats right seeing that the 8 wasnt part of those

[trail tendon]

yes

[empty quartz]

and that the 25 appears to be from the right traingle being the hypotenuse

[trail tendon]

so whats b

[empty quartz]

7

[trail tendon]

yes

are you able to get the area of each side and add em all up for the surface area?

[empty quartz]

confused

so i could begin the box thing i was trying to do before?

[trail tendon]

um

i'm not sure what the box thing is

you know what surface area is?

[empty quartz]

maybe

like total surface area

thats LSA + 2B

b is b x h

so 7 x 24 to find the b and then divide it by 2

so 168 would take 2b and then i would have to add the LSA

this is an example i found that uses pyth

[trail tendon]

but there are two bases with the same area, no?

[empty quartz]

pretty sure all the rectangles are different

wait

nvm tthey the same

[trail tendon]

aren't we talking about the triangles lol

[empty quartz]

so if 25 is the edge, would that be the constant number used for hte box

like the boxes for finding the surface area

im so confusing stg

[trail tendon]

🤣

how many surfaces are there

[empty quartz]

3?

[trail tendon]

in total?

[empty quartz]

if we including those triangles then 5?

[trail tendon]

yeah

[empty quartz]

ok so 5

[trail tendon]

its so strange to me that you think of lateral surface area before total surface area 😂

[empty quartz]

yeah because i need the LSA to find the TSA

its LSA +2B = TSA

[trail tendon]

i guess...

although

[trail tendon]

this isn't always true

but whatever

good enough lol

[empty quartz]

lmao

can u possibly walk me throughon how to get the answer

cause tmrw on the quiz, theres one question for each shape, so if i know hat to do with these mfs, ill do fine on it

[lime dune]

“lateral surface area” is just any part of the surface area that isn’t a base

[trail tendon]

yeah

[empty quartz]

huh

[lime dune]

above, you have a right triangular prism - that is, the right triangle faces are the bases

[empty quartz]

ok so there are 3 LSA

[trail tendon]

by the way, i never really completely understood, how do you know if something is a "base"?

[trail tendon]

but 5 TSA

well

5 sides

for TSA

[lime dune]

if it’s a prism

then that’s like taking a 2D shape and “stretching”/“extruding” it out into 3d

a cylinder for example

[trail tendon]

what if its not?

[empty quartz]

so could u walk em thru on how to get that

[lime dune]

if I take a circle

and stretch it out

the other relevant case is pyramids/cones

where it should be quite obvious which face is the base

[trail tendon]

what's the area of the front side

[trail tendon]

yea

[lime dune]

the one that doesn’t have the apex as one of its vertices

[empty quartz]

84

24 x 7

/2

=84

[trail tendon]

thats the area of each triangle

yes

[empty quartz]

so 168?

[trail tendon]

yes

[empty quartz]

cause 2b is 2(84)=168

ok

so

what do i do to find teh LSA

or heres a better one, how should i do it in forms of those god damn boxes

[trail tendon]

find the area of all the sides and add them up

[empty quartz]

or multiplication

[empty quartz]

huh

[trail tendon]

the area of a rectangle is bh

[empty quartz]

so wait

24 x 7, 25 x 7 and 8 x 7?

and then add those?????

[trail tendon]

yes

💀

and the areas of the triangles

[empty quartz]

and those are the #s right

so 168 + 175 + 56 + 168

[trail tendon]

oh its uh 25 * 8, 24 * 8, 8*7

mb

[empty quartz]

BUT WHYYYYYYY

i dont visualize it properly

like wtf

[trail tendon]

oh 1 sec

[empty quartz]

is it because of the 8

like what does the 8 need to look like to do it

and connect to all 3

like wtfffff

and this vocab has me braindead

[trail tendon]

idk if this helps

💀

[empty quartz]

but why is the 8 the main # involved into the boxes

[trail tendon]

you may be having hard time the 3D

[trail tendon]

don't worry about that

its the height

[empty quartz]

ahhhh the fucking height

god damn it

my dumbass

[trail tendon]

you see the rectangle that has area 8 * 24?

[empty quartz]

its base times hieght like u said

god damn it

yeah

yep

[trail tendon]

💀

and the rectangle that has area 8 * 25?

[empty quartz]

thx for that pic

[trail tendon]

yeh 💀

[empty quartz]

so 8 x 7, 8 x 25, 8 x 24

so 592

is the TSA

[trail tendon]

you forgot to add the triangles i think

[empty quartz]

Nah that’s adding the utraingles

[hollow moth]

how should I learn geometry better? I can't wrap my head around it ngl

[subtle zenith]

Me too

[lime dune]

without a more specific question there's not much i can say without it being meaningless generality

[faint pasture]

sometimes alll someone wants is the meaningless generality tho fr

[lime dune]

bleh

then

draw good diagrams

[hoary totem]

https://x.com/LongFormMath/status/1795935120261525848?t=hAsq4bv3Hy1puvob3cKueQ&s=19

Jay Cummings (@LongFormMath) on X

Here is a lovely geometric proof that sqrt(2) is irrational.

The proof begins by looking at an isosceles right triangle whose legs have length 1. By the Pythagorean theorem, this triangle's hypotenuse will have length sqrt(2).

Twitter · May 29, 2024, 9:47 PM

cool proof

[nocturne remnant]

my immature ass will laugh at the account name

[grand sail]

What is trigonometry

[faint pasture]

well at the most basic level it relates the sides of a triangle

[grave pond]

Generally functions that relate angle measures to ratios between lengths.

[grand sail]

So, why do we need a raios of sides

[faint pasture]

and then whatever mess it becomes when you reach non euclidean shit

[grave pond]

For example if you know one of the sides and want to know the other.

[faint pasture]

for this triangle if you are given QK = 2, how would you find PK? the answer is with trigonometry

[grave pond]

(That's a somewhat bad example because for those particular angles you could also say "reflect the triangle across PQ, and that will give you an equilateral triangle").

[grand sail]

Im confused, trigonometry represents a ratios of sides (i have there only angles)

[grave pond]

You were also told the length of QK.

[faint pasture]

i mean it is the simplest one, for a 45-45-90 triangle it is easier cuz isoceless, then we reach 18-72 or 37-53 but those are just weird xD

[obsidian harness]

yes

if your triangle has side lengths x, y, z for example

you can make each side k times larger, and it will still be similar (look the same but bigger/smaller)

So our new side lengths are kx, ky, kz

Check that (kx)/(ky) = x/y and so on, so the ratios between sides are the same

[faint pasture]

(isnt similarity taught before trig?)

[obsidian harness]

it should be

[faint pasture]

hm yea

[obsidian harness]

Hopefully this will be revising old stuff rather than teaching them new info

[faint pasture]

true

[grand sail]

I do not understand what role play angles in that (are they sin,cos,tag

[faint pasture]

they just relate a particular ratio
for eg if your triangle has the angles 30-60-90
and you take one such triangle and measure the ratios
you can use all those ratios for all triangles with same angles
this is applicable to all other angle pairs too (must contain a right angle though)

[faint pasture]

(btw is helpful role only for those who help in the help channels or everywhere?)

[tame helm]

try watching this vid https://youtu.be/PUB0TaZ7bhA?si=aKzdEz6_IYYQ1VZT

[willow arrow]

Hi guys I have a question that I will get from proofs and logic to here, which is if circle has zero sides or infinite sides?

[obsidian harness]

can be in other places

like pre-uni, early uni, advanced doesn't give helping activity though

[obsidian harness]

depends on what you mean by 'side'
it's an interesting question

[faint pasture]

depends

[faint pasture]

if not there then whats the other places 💀

[obsidian harness]

don't think there are any other places

maybe help forum? ask the mods

[faint pasture]

hmm i guess ill wait for when one comes active

[faint pasture]

reminds me of the whole klein bottle thing, does that thing have zero volume orr infinite volume

[obsidian harness]

I've asked in #『meta-discussion』

[willow arrow]

Ya so I got a grand disagreement from someone, I kept telling them it is based off how you define sides, but they kinda just went forth wall and defined circle as something that doesn't have Exterior angle...

They presented a proof for that as here ->

 Intuitively let's define circular shapes like circles, ovals and such as an object with 0 external angles. Then :
Ea = 2pi/n
n -> inf
Therefore, Ea -> 0
I'm doing unecessary extra work here; either show what is wrong with my statement above or there's no problem with my assertion.

Now I got no clue how this answers or helps up with idea related to "sides" but
i do gladly define "side" as a line segment with 2 of its endpoints on 2 vertices.

Different compositions of these "sides" can make up different shapes Ig.

But I think I am going off the track pretty quickly..

So is that proof even right approach?

[obsidian harness]

#『meta-discussion』 message

answered

[willow arrow]

I suppose this is the correct channel to ask the question.

[grave pond]

Why are you hiding your definition behind spoiler markup?
With that definition it should be fairly obvious that there are no "sides" in a circle.

[obsidian harness]

that really sucks that the goddamn help forum counts but these channels don't count

[faint pasture]

but the thing is normal discussion regarding the subject also happens here

soo there is no way to really differentiate is there

[obsidian harness]

shit

fair enough but I think we should loosen the definition of helping a bit

like giving info about a subject also should count as helping

[faint pasture]

i mean maybe but like if you look at #calculus half of the times its just people ranting about how leibniz notation sucks soo i mean you wouldnt wanna give them the "help points" xD

[willow arrow]

Sorry mb marked it behind spoilers.

I actually had the definition which was pretty vague was accepted by the other end anyways.. which was "line segment == side." But I retracted that one back.

And yes, I definitely agree it should just make it zero sides by definition, so even if someone asks me to "prove it has zero sides" I could just say circle is by definition having zero sides / no sides, unless they want a different definition.

With that out of the way, I was confused if the later approach with external angles is conceivable. Cause it doesn't really talk about sides anymore.

Fixed the spoilers part, it's italics now.

[willow arrow]

Guys tell me if I am getting trolled or smth... the suspense is haunting.

[dry scaffold]

]

[cold stream]

how does it equal this?

[grave pond]

It's not really a mathematical question.
In the commonly understood usage of the words, the word "side" only has a clear meaning for polygons, and a circle is not a polygon. Anyone who wants to even use it about a circle will need to provide a definition of what they mean; depending on which definition they pick they may end up with something that the circle has none of, or one of, or infinitely many of, or perhaps something in between. Choosing between the possible definitions is not something that mathematics as such has an answer for; it is up to whoever picks a definition to convince their listener that "side" is a reasonable word to use for whatever they're talking about.

[trail tendon]

a circle is just one curved line segment :>

💀

[willow arrow]

Alright man, glad to hear it's all about picking definitions and basically agreeing with specific definitions.

I appreciate your assessment.

[willow arrow]

Definition moment.

[trail tendon]

😂

[lime dune]

wdym by "curved" ☝️🤓

[obsidian harness]

Wittgenstein.....

[grave pond]

Darüber muss man schweigen?

[devout breach]

i’m literally so bad at math

i don’t think i’m doing this right

[atomic tulip]

,calc 900/2

[somber coyote]

Result:

450

[devout breach]

HELP-

[atomic tulip]

Is 900/2 not being 300 not enough help?

[devout breach]

i said help as in lol

[trail tendon]

help

[tropic flame]

<@&286206848099549185>

[golden whale]

hi

y

[tropic flame]

R u helper

[rapid shore]

What is the problem?

[golden whale]

yep

[tropic flame]

Can u help me with hatd question perimeter

[rapid shore]

Sure. Where is it?

[golden whale]

send it to what is it

[tropic flame]

No help me understand it

[rapid shore]

What do you need to understand?

[golden whale]

can you say the topic in academic form

[lime dune]

what is the problem

[tropic flame]

No

[lime dune]

!original

[lime crown]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[golden whale]

so which topic you wanna know

😶

[tropic flame]

Area and volume

[golden whale]

yeah for sure shall we have it in voice ?

[tropic flame]

Yh

[golden whale]

it would be easier

[tropic flame]

Alr

[faint pasture]

dont steal my name

[rapid shore]

This is a math channel.

[grave pond]

Sure.

The results look right, at least.

With a bit of experience you can do the angle conversion faster than the step-by-step arithmetic you used here, by viewing the fraction of pi as a combination of pi/1 (=180­°), pi/2 (=90°), pi/3 (=60°) and pi/4 (=45°).

[devout breach]

thanks

i’ll prob just leave it like that because that’s how we did it in class

i have two more problems i might ask about after i just need to do them first

[faint pasture]

It is possible but not really doable by hand

Some computers graph it sure, others use what is called a "taylors series" to approximate the value

Well it is kind of complex to explain if you dont know the basics of calculus
But it is basically an infinite termed polynomial which is equal to a function

Well yea thats when you need calculus knowledge to understand the working

Im not aware of that tbh

Well do you know basic differentiation too?

Um the actual definition for the taylors series is based on differentiation so yea

He probably just approximated it by drawing the triangle but im not sure

I guess graphs werent a thing back then eithee

So triangle is the only real way

Or maybe just approximations

Like sin45 = 1/sqrt(2) we can write sin 45 solely in terms of sin1

Soo we can approximate sin 1 from there

And then calculate all other values

But it is gonna be tedious if not impossible to solve a 45 degree polynomial xD

[trail tendon]

dude i thought you meant 45 degrees 😂

i was like "bro its sqrt(2)/2, already calculated" 💀

[faint pasture]

Lmfaooooo

[faint pasture]

No wait

I did mean 45 degrees in there?

[trail tendon]

oh

i mean true

wait

[faint pasture]

I am saying you can calcullate sin 1 degree from there

And calculate all other shit after that

[trail tendon]

using series decomposition?

[faint pasture]

What even is that 💀 like taylor's series right?

It is

[trail tendon]

yeah