geometry-and-trigonometry

[humble pulsar]

which is: slope of the base and line equation for the base, line perpendicular through the other vertex, find the intersection, then distance formula

[fresh pike]

what does a line above 2 letters mean again?

Does it mean line or side?

[grizzled lantern]

@fresh pike segment

[fresh pike]

oh okay thx

[fresh pike]

can someone show me how to determine which angles are bigger than the others?

and on this one, how do i find out which one is the longer side?

[earnest echo]

The side just infront of largest angle is largest

[fresh pike]

infront?

[earnest echo]

This one is better

[fresh pike]

what am i even looking at lmao

[earnest echo]

Here side c is infront of angle gamma

Ignore the other working

Just look at the traingle

[fresh pike]

so for this one how would i go on about solving it?

[earnest echo]

Well, you see angle GHJ is 90*

[fresh pike]

so the largest side would be HJ?

[earnest echo]

No

[fresh pike]

hmm

[earnest echo]

What's the side infront of Angle GHJ?

[fresh pike]

the lesson that taught me how to find the longest side was very vague and brief in its wording

what do you mean by infront?

[earnest echo]

Here side GJ is infront of angle GHJ

[fresh pike]

man i don't get what infront means lmao

[dark sparrow]

opposite

godfather means opposite

@fresh pike @earnest echo

[earnest echo]

(All these years of English education in drain)

[dark sparrow]

down the drain*

[earnest echo]

[nocturne junco]

Hello, I was doing my trigonometric problem that seemed easy at first then i eventually realized that I assumed that the hypotenuse of x and y legs is equal to the m. Is there a way to verify that the red triangles form an isosceles triangle?

[dark sparrow]

i dont think they do

[rigid dove]

Guys

Is anyone good with proofs?

I need help with a question 😭

[dark sparrow]

i'm sure there exist one or two people good with proofs in a server of thousands

is it a two-col proof question

[rigid dove]

Here ill take a picture and put it here

Please dont mind the pomegranate juice

[dark sparrow]

,rccw

[rigid dove]

Any ideas?

[dark sparrow]

aight so this is a two-col proof

im not going anywhere near those personally sorry

[rigid dove]

😭

[dark sparrow]

youll have to find someone else who doesnt have an aversion to them yet

[rigid dove]

Ur kinda speaking gibberish to me 😂

But its fine thank u for looking

Im sure someone will turn up

[upper karma]

You can say FM = MC but idk the reason

maybe 'midpoint' would be the reason

[upper karma]

AF to FM to MC to CD
FM and MC are equal as M is the mid point
and since you know AF and CD are equal vectors, therefore AM is equal vectors to MD,

@rigid dove

because you start from M, and then you move from M to D, and that would require you going to MC then CD (which MC is equal to FM due to it being the mid point) and CD is equal to AF (as it is stated in the question)

so essentially, AM and MD is equal as essentially being added the same vectors from M

[dark jacinth]

Anyone know how I would go about finding a point thats not on the x axis?

[upper karma]

it would help to involve circles into this

@dark jacinth

[dark jacinth]

I prefer using a parabola

[upper karma]

https://tenor.com/view/thatll-work-nodding-zach-zach-galifianakis-gif-5886339

yeah actually, a parabola seems like a very clever idea

[dark jacinth]

that would accuratly show all points that are twice as far from (0,0) than (6,0), but I ma not sure how to do that

[dark jacinth]

do you know how I would go about calculating the parabola

[upper karma]

wait

couldn't you make equation of Pythagoras?

[dark jacinth]

how so?

[sand sedge]

Hello English isn't my first language; i can't find the meaning of 'a dashed ray' in contrary with just a ray.

Nvm. it's the form of the line; dotted, dashed, pointed etc.

[upper karma]

Anyone can help me with this? i need to solve the lengt of the river

[dark sparrow]

what have you tried & where are you stuck

[upper karma]

Tried the Law of sines

but cant get it to work

[dark sparrow]

you tried the law of sines to get what

[upper karma]

The oppsoite side of 460m

[dark sparrow]

the opposite side?

this is a triangle

no two sides are opposite to one another.

[upper karma]

i know

of course

[round isle]

use the law of sines

[upper karma]

Haha just wrote that i tried that

but i bet im doing something wrong

or putting the numbers in wrong places

thats what i need help with

lol

[dark sparrow]

can you show your work then

just to make sure you are on the right track here

[upper karma]

Well i removed it becouse it was wrong lol

[dark sparrow]

can you redo it

[upper karma]

Well here you have what i did lol

https://gyazo.com/e47e9959b0a7cab5a35e1c7cbcfe2718

Thats why i asked here becouse i aint got no clue how to solve it

[dark sparrow]

i am assuming b is the side you circled in blue

[upper karma]

yep

[dark sparrow]

you should have had sin(68)/460 = sin(71)/b

which would then give you b = 460sin(71)/sin(68)
and then the height of the triangle is just b sin(41)

[upper karma]

Lol thanks

That easy

My brain got some error issues sometimes i guess

[flat viper]

the two sides will be equal since it is an isosceles triangle
@round isle is it answer to my question?

The lengths of two legs of an isosceles triangle are represented by the expressions (3x - 7) and (x + 5).

The perimeter of the triangle is 40cm.

Find the length of the base of the triangle.

Do NOT label your answer.
@!! リℸ ̣ 𝙹リℸ ̣ ⍑ᒷℸ ̣ ∷ᔑᓵꖌ#0001 is it answer to me?

[silent plank]

if all those expressions matched the setup in your question then probably

[flat viper]

no, but its under my question lol

so maybe im dumb to understand

[silent plank]

oh misread the actual quote

the two sides will be equal since it is an isosceles triangle
yes that is aimed to help you with that question

[flat viper]

how do we know it is isosceles

[silent plank]

because you are told that it is

the first line in the question

The lengths of two legs of an isosceles triangle are represented by the expressions (3x - 7) and (x + 5).

[flat viper]

hm its not my question

ok sorry then it wasnt for me

[flat viper]

pi < x < 3pi/2 and 3sinx-5cosx = 0
cos^2.x - sin^2.x = ?

[dark sparrow]

what are those dots?

[flat viper]

times

its okay i solved

help please?
@flat viper this not yet

[fiery sundial]

How do I prove (secθ-1)(secθ+1) = tan²θ?
Here's the best I could do:

Subtract Fractions: (1-cosθ/cosθ)(1+cosθ/cosθ) = tan²θ
Multiply Fractions: 1-cos²θ/cos²θ = tan²θ```
I need to get sinθ in the mix somehow

[crystal charm]

@fiery sundial start with (1/cosθ - 1)(1/cosθ +1), put everything to the same denominator, and multiply
Never say (1/cosθ - 1)(1/cosθ +1) =tan^2(θ) to start your reasoning : it is true so the only answer you can find following this method is.. 1=1

[fiery sundial]

Yeah, it's a proof

I'm trying to get it to equal tan²θ

[silent plank]

you're missing parentheses in multiply places

also this depends on what you;re allowed to use

do you know your pythagorean trig identites?

[fiery sundial]

Learned them today

Technically yes

Do I have practice with them no

[silent plank]

they're used in the vast majority of these proofs

[fiery sundial]

I see that I can replace cos²θ with 1-sin²θ though

[silent plank]

that is one option

but doesn't really help that much

what else can you get from that identiy

[fiery sundial]

Oh!

sin²θ = 1-cos²θ

Which is something I have

And that brings me to my answer

Thanks a bunch!

[silent plank]

also note that you could also expand the intial expression directly

to get sec^2(theta) - 1
which is tan^2(theta)
(from another pythagorean trig identity)

[livid plume]

do tangency to the circle + similarity of triangles questions belong here

[silent plank]

yes they do, alternatively use a free channel under math-help

[livid plume]

well i'm having a bit of trouble with this one

[silent plank]

look up some circle geo theorems

do you have access to a list?

[livid plume]

a list? not that i'm aware of

[silent plank]

they should be in your book on in notes your teacher should've given you

or you can find a convenient summary of them online

[livid plume]

tangency of the circle belonged to the curriculum of last year which got cancelled

there are some left over questions about that in the new book so

[silent plank]

ok. look up some circle geo guides online.

you should also familiarise yourself with terms like chord,secants etc.

here you'd want to relate the tangent AB and secant AC,
which could by done by applying the conveniently named tangent-secant theorem

[livid plume]

would the euclidean theorem formula work in this situation

nevermind i got it

used euclidean

[silent plank]

you mean pythagoras?

that would also work

[livid plume]

did (AB)² = AD × AC

[silent plank]

oh, that's the tangent-secant theorem

euclid is very broad

[livid plume]

i suppose so

thank you for your help 👍 👍

[sharp plume]

How do I do G

It is in an orthonormal axis system

And btw how do I know if a vector or vectors are standardized

Exercise 2a

[west basin]

to standardize a vector you are gonna wanna multiply by the vector by a scalar consisting of 1/|v|

so just divide each component by the magnitude of the entire vector

@sharp plume

[lament shell]

pls help

[upper karma]

What have you tried so far

[lament shell]

um

im not sure if this is right but

i did 180-72 = 108

so is it 108?

@upper karma

[upper karma]

No

But okay

Let's start by the upper triangle

What properties does a isosceles triangle angle-wise?

ie what can we conclude about the angles on a isosceles triangle

[lament shell]

ok

sorry

um

2 sides are equal

so two of the angles have to be the same

@upper karma

is anyone else here to help me?

[humble pulsar]

yeah, angles opposite equal sides are equal

[lament shell]

ok

wait so x is 72?

[upper karma]

is anyone else here to help me?
Are you srs? If you take 5 minutes to answer it's okay but if i take 4 you complain

jeez

[lament shell]

i wasnt trying to be harsh

[upper karma]

Be patient is what i mean, i can't stand there 5 minutes sometimes waiting, for then to answer inmediately

Anyways

[lament shell]

ok sorry

[upper karma]

The opposite angles of the equivalent sides are equivalent

Would you be able to point where the other 72° angle would be at?

(in the upper triangle)

[lament shell]

ok

[upper karma]

Yes

So now would you be able to find the last missing angle at that upper triangle?

[lament shell]

would it be 36?

[upper karma]

,calc 180-(72+72)

[somber coyote]

Result:

36

[upper karma]

Yes

And now we move to the lower triangle

If we know that the big angle is 90° (because of the square), and we know that one part of the angle is 36, what would the other part of the angle be equal to?

[lament shell]

180 - 126 = 54

[upper karma]

Wait huh

Where does the 180 come from

[lament shell]

wait

which angle are we talking about

[upper karma]

The one at the middle right (with a square on it)

[lament shell]

oh

its 54 right?

[upper karma]

Yes

Because 90-36=54

[lament shell]

yeah

[upper karma]

And now last step

[sharp plume]

@west basin can u explain how to do

[upper karma]

What do we know about the angle BCP

(considering we know that it is an isosceles triangle)

[lament shell]

that one of the angles is 54 and that 2 of the sides are equal

[upper karma]

Yeah i mean

We know it is isosceles, hence 2 angles are going to be equivalent as the previous triangle

Which 2 angles are gonna be equal on this triangle

[lament shell]

B and C

would you just do (180-54)/2 and that would be the angle for both of them?

[upper karma]

That's not how you name angles, B and C are points

But either way, i know what you mean and no

[lament shell]

Oh BC

[west basin]

ok i can give a short example if you had a vector like v = (1,2,3) you would calculate the magnitude, |v| = sqrt(14) then divide each component by the magnitude so v_n = (1/sqrt(14), 2/sqrt(14), 3/sqrt(14))

@sharp plume

[upper karma]

CBP is an angle, PCB is another angle and BPC another

The letter at the middle, for example at PCB, C is the point where that angle is located

[sharp plume]

ohhh i seee now

[lament shell]

ok

[upper karma]

Okay but look at this

[sharp plume]

what about AB, A(1/2,o,o) and B(0,1/2,sqrt(2)/2) @west basin

do i have to multiply A and B

[upper karma]

@sharp plume i'd appreciate it you 2 take your q to another channel

[sharp plume]

yes

[upper karma]

@lament shell if you look at this pic, remember that the opposite angles are equal

Do you see how i know now that PCB and BPC are equivalent?

[lament shell]

umm

[upper karma]

umm what

[lament shell]

well arent they just a diffrent order of the same angle?

[upper karma]

What?

I'm not sure what you mean

[lament shell]

like isnt CPB equivalent to BPC?

WAIT

[upper karma]

You read it wrong

[lament shell]

um

im confused still

[upper karma]

The letter at the middle, for example at PCB, C is the point where that angle is located
Always remember this

Pinpoint your confusion

[lament shell]

ok

why does it matter what letters in the middle?

[wise hornet]

technically you ppl have been talking about the same triangle this whole time

angles have hats on

[upper karma]

This is how we name angles

The letter in the middle is going to indicate the point where it is located

You can also think of it this way

The angle PCB, is the angle that forms PC and CB

[lament shell]

i think im getting confused cuz i think we are still solving for x but we arent right?

[upper karma]

We are indeed

But i had to name the angles in a way it could be understood

Instead of saying: "the angle at the top" "the angle in the middle left below the triangle", etc

Which is obviously worse

Okay if this system is confusing you, let's just name angles to a letter

Would you be more comfortable with that? @lament shell

[lament shell]

yeah

[upper karma]

Missing ° but anyways

Forget about the letters naming and all that

Do you understand why we can say now that the angle y is equal to 54°

[lament shell]

just because its on the oppsite side?

[upper karma]

Yes

[lament shell]

but isnt y opposite x?

[upper karma]

Wdym?

[lament shell]

is the green line shows the opposite or is the orange one the line

[upper karma]

The greenish line is just me showing which side it is opposite to y

The orange line is just me showing which side it is opposite to the 54°

[lament shell]

wait so is x the only one thats not equal because both its sides are equivalent?

[upper karma]

I mean yeah, x is not the opposite of any of the equal sides

Angles y and 54° are opposite to the sides that are equal (because of the | mark)

[lament shell]

OHHH

ok i get it

[upper karma]

So y is the angle that is equal to 54, so we can just do this

Hold up

Now do you know how we can finally find x

[lament shell]

180-(54+54)

[upper karma]

Yes

Good job

[lament shell]

72

[upper karma]

Yup

[lament shell]

wow

ok

thank you

sorry if i was a little slow to understand lol

[upper karma]

Don't be sorry

It's all good

[lament shell]

Alright thank you

[upper karma]

Yw

[wary gate]

https://cdn.discordapp.com/attachments/363224154469826562/777985147370340369/unknown.png

do I just add 360 or subtract it?

And thats the answer?

[upper karma]

yeah

[slender nacelle]

@upper karma use the fact that radius of this circle (distance between origin and point P) is unity.

Is cot positive in quadrant 2?

Yes!

You figured it out. Congratulations

Convert the given equation in the form expression in the question

[silent plank]

completing the square

18/2 will be part of the process

$\cts$

[somber coyote]

ramonov:

[silent plank]

will be part of the process

they want an equation in the form:
something squared = something

yes

[exotic fjord]

hi

[silk zodiac]

what does cos(wt-kz) when it becomes an exponential?
e^(wt-kz)
or e^(wt-jkz)?

[round isle]

are you talking about complex exponentials?

[civic crown]

hi can i have help

[round isle]

yes

[upper karma]

solve each equation for the function... Problem = x^4-10x^2+9=0

can someone help me with that

[polar whale]

Use substitution t = x^2

Then u got a quadratic equation which u can solve

U will get 2 solutions t_1, t_2 which each have 2 solutions for x because t=x^2

@upper karma

[upper karma]

@polar whale didnt follow the first part

[polar whale]

Like i said use substitution

Set t = x^2

[upper karma]

ok

[polar whale]

Then what do you get ?

[upper karma]

I Could Use Some Help, Heres An Example Of What Level/Type Of Math I'm Doing

[slender nacelle]

What do you need help with?

[upper karma]

I Don't Understand How To Determine If It's SSS AAS ASA Or SAS

[fresh pike]

how do i figure out which is greater

or which is lesser

oh shoot, someone already posted something before me woops

[slender nacelle]

What does tour intuition tells you? @fresh pike

[fresh pike]

at first i thought it was AB < De, but i think that's wrong

[slender nacelle]

It is correct

[fresh pike]

what the

i swear there was something i had to do with the angles

[slender nacelle]

Both sides are same. If the angle between them is more, that means other side is more

[fresh pike]

i might look back on the other lessons and post it here to ask for help

Oh yeah i see now

but there was other ones were I applied the same thing i did for this one, but it was wrong

[slender nacelle]

You can share these problems as well

[fresh pike]

def will later

[slender nacelle]

Sure

@upper karma S=side, A=angle. Are you familiar with that?

[upper karma]

Yeah I Know What They Stand For But Nothing Else Really

[slender nacelle]

So SSS would mean three sides of a triangle is equal to a different pair of sides of a different triangle

SAS would mean that two sides and angle made by those two sides is equal

And so on. @upper karma

[fresh pike]

oh yes for this one

how would you find the answer for this one?

im sure it's easy, but I guess i missed out on something

[slender nacelle]

Do you know sine rule?

[fresh pike]

Nope, could you explain?

[slender nacelle]

Fir any triangle ABC, a/sinA = b/sinB = c/sinC

Here sides are defined BC =a, AC = b, AB =c

[upper karma]

@spark star

[fresh pike]

how do i determine which angles are the specified angle names

[spark star]

Hey guys.

Does this make any sense?

[humble pulsar]

yes it does

[spark star]

Can you explain?

[slender nacelle]

Here, A= 20 degrees, B = 110 degrees @fresh pike

[spark star]

They are congruent.

[humble pulsar]

explain what?

[spark star]

I see that.

How it works.

[humble pulsar]

they're congruent

[spark star]

Yeah.

[humble pulsar]

it's F pattern iirc

[fresh pike]

Here, A= 20 degrees, B = 110 degrees @fresh pike
@slender nacelle Okay im following

[spark star]

2x-6=3x-20

[humble pulsar]

yeah

[spark star]

x=-14

[humble pulsar]

no

[spark star]

x=14

[humble pulsar]

yeah

[slender nacelle]

So if you use a/sinA = c/sinC @fresh pike

[spark star]

That doesn't make sense

3x-20
42-20 = 22 degrees

[slender nacelle]

You’ll get a/c = sinA/sinC =sin 20/sin 50 <1
So a<c

[humble pulsar]

most drawings/diagrams arent to scale

[spark star]

I see.

So, I did get it right?

[humble pulsar]

yeah

[upper karma]

[spark star]

The drawing is confusing.

[slender nacelle]

Sorry we have to compare b amd c

[fresh pike]

so we completely ignore the B?

oh sheet internet slow

[humble pulsar]

That's why you trust the math, the drawing is to aid @spark star

[slender nacelle]

But b/c = sinB/sinC = sin 110/sin 50 = sin 70/sin 50 > 1

So b > c or AC > AB

[fresh pike]

what do those "/" represent?

[slender nacelle]

Division

[fresh pike]

wuh we divide,

i might just look up some khan academy videos

and try to apply your words to the videos and see if it helps

[humble pulsar]

Law of Sines: $\frac{\sin{A}}{a}=\frac{\sin{B}}{b}=\frac{\sin{C}}{c}$

[fresh pike]

thanks anyways 👍

[inland canyon]

aye bruh

can yall tell me something simpl

[slender nacelle]

Sure, you’re welcome

[somber coyote]

moshill1:

[inland canyon]

wtf do i do if its like

56π

cuz like

it ype 56 in my calculator then hit π

and it only shows me pi

[somber coyote]

moshill1:

[inland canyon]

@slender nacelle ur the only active person i see

[slender nacelle]

I think you have to multiply it by pi and press =

[inland canyon]

ye thats what i thought

but like

my work says

"dont type 3.14 unless told to, just the π button on ur calculator"

and im like bruh

pie is 3.14

well i mean its more than that

but bruh

[slender nacelle]

Pi is not 3.14

[slender nacelle]

Yes you will get more accurate results if you use more digits

[fresh pike]

it was wrong, I just need to figure out why

[inland canyon]

bruhy i mean

i just need 3.14 for rn i think

[slender nacelle]

So b > c or AC > AB
@slender nacelle @fresh pike

[inland canyon]

wait so is pi just never ending?

[slender nacelle]

AB<AC

wait so is pi just never ending?
@inland canyon yes

[inland canyon]

thats pretty poggers i guess

[slender nacelle]

It is what it is lol

[upper karma]

@fresh pike size of a side is dependent on the opposite interior angle, longest side of a triangle is always opposite the largest interior angle

[fair marten]

how do u do this

[round isle]

use law of sines

[dim gyro]

So I don’t ever remember having a problem like this one

[hollow haven]

is anyone free

[round isle]

draw a line from center of circle to D and C

[hollow haven]

i need help with a question

[round isle]

then draw a line from center of circle to A and B

sorry not C but the other side where the triangle is tangent to the circle

[dim gyro]

Like this?

Also would line AC be the same length as CB

[round isle]

you get similar triangles

[hollow haven]

wait could i quickly ask a question @round isle

[fair marten]

how do you do this?

[round isle]

didn't I just tell you how to do this?

@hollow haven yes

[hollow haven]

if arg (z+2) = 1/2 pi and arg (z) =2/3 pi, find z

its complex numbers

[hollow haven]

use this @fair marten

[round isle]

you could use the formula for arg

[spark star]

Is this congruent?

[round isle]

you'll get two simultaneous equations

let z = x + iy

[spark star]

Waif if this is congruent

Does it Mean

2x-12=3x-8

[hollow haven]

formula for arg is tan y/x tho

[spark star]

What do I do after

2x-12=3x-8
@spark star

[round isle]

it's atan

not tan

[hollow haven]

i havent learnt arctan yet

[round isle]

what do you mean you haven't learnt arctan?

[hollow haven]

can i send u my teachers working

[round isle]

it's the inverse of tan

[hollow haven]

what do you mean you haven't learnt arctan?
@round isle in the UK, we dont learn it till later

meaning its doable without it

[round isle]

you know about sin, cos, tan but you don't know their inverse?

[hollow haven]

not yet

uk curriculum is different x

d

[round isle]

right

[spark star]

2x-12=3x-8

Do I combine like terms?

[hollow haven]

if it helps i have some working out

[round isle]

so did your teacher show you how to do this by using exponentials?

[hollow haven]

i honestly have no clue

we drew it on an argand diagram

@spark star

[spark star]

Hm?

[hollow haven]

(2x-12)+(3x-8) =180

[spark star]

They are congruent.

[hollow haven]

because a straight line = 180 degrees

[spark star]

But there is two.

The top and the bottom.

[fair marten]

can someone step this out with me

[hollow haven]

did u not use the formula?..

[round isle]

can we call admin to report someone for spam

[fair marten]

i don't get the formula

[hollow haven]

LOl

ok sure

[round isle]

@fair marten do not spam

[hollow haven]

i don't get the formula
@fair marten ok, have a read on bbc bitesize about the sine rule and how to use it

for a start

[round isle]

this is so bizarre @hollow haven

[hollow haven]

lol

[fair marten]

alright

[spark star]

I'm sure you can't add to 180@hollow haven

[hollow haven]

i have no clue what my teacher do

[round isle]

I don't recall the geometric method for solving this

[spark star]

Correct me if I'm wrong

[round isle]

damn

probably because I never used it after finding out about atan

[hollow haven]

thing is i havent really looked into congruent triangles in my school in uk

probably because I never used it after finding out about atan
@round isle try it with atan and see if the answer is the same

[round isle]

I mean, atan is literally just the inverse of tan. You take the tan of an angle and you take atan of the ratio of sides that define the tan

try it, it's very simple

[hollow haven]

ok will do cheers

[fair marten]

so 180-116

is the correct answer 64

[hollow haven]

try it

I mean, atan is literally just the inverse of tan. You take the tan of an angle and you take atan of the ratio of sides that define the tan
@round isle if u are still interested, its just trig LMAO

so 180-116
@fair marten assuming u put the angles and side lengths into the equations, probably. 64 sounds correct

[fathom root]

https://gyazo.com/ded8412c79fe7142f98d2a4c2959c5c3

am i stupid or stupid

😆

anyone know what im doing wrong for the second part

[untold peak]

could someone help me with this question?

"A construction engineer determines that a straight road must rise vertically 45 m over a 250 m distance measure along the surface of the road (the straight road represents the hypotenuse of the right triangle).  Calculate the angle of elevation of the road."

I just can't for the life of me figure out how to draw the triangle for that

I don't understand what it's asking me

it is a right angle triangle I know that much

[fathom root]

i can draw it for you!!

[glass rover]

csn someone help me witha question

@fathom root if your available

\cot\theta>0 \text{ and } (\tan\theta)(\sin\theta)<0
cotθ>0 and (tanθ)(sinθ)<0

o woops

[fair marten]

can i get some help

i can't wrap my head around proportions

i tell you hwhat

[slender nacelle]

Do you know which length would measure up to 9.3, other than what is mentioned in the figure?

[zenith anchor]

Do you know which length would measure up to 9.3, other than what is mentioned in the figure?
@slender nacelle I received help, thank you though!

[untold peak]

Does anybody know if the shadow would be the hypotenuse or the adjacent? I can't figure it out

"A communication tower casts a shadow of 55 m when the sun is at an angle of elevation of 72°. What is the height of the tower to the nearest metre? Include a diagram in your solution."

also thank you @fathom root for earlier

big help

[zenith anchor]

adjacent

[untold peak]

now how does that work?

would the opposite be considered the tower?

[humble pulsar]

yes

[untold peak]

ok

[zenith anchor]

exactly so

[humble pulsar]

Include a diagram in your solution would help

ie make a diagram

[untold peak]

I don't know how that works

[humble pulsar]

you dont know how to draw?

[untold peak]

if the angle is the sun and it's facing up at the tower then how does it make a shadow

nonono

I can draw

just what I said above

sorry network lag

[humble pulsar]

Z pattern

[untold peak]

I'm still confused

sorry I just have a hard time understanding math

[humble pulsar]

Z pattern ^

[zenith anchor]

how about this

its not the sun facing up lol

either way

damn idk how to explain this

1 second

[untold peak]

ok

I appreciate it though

even if I can't understand it knowing that the shadow would be the adjacent is good enough for me

thank you @humble pulsar

[humble pulsar]

that's not the best mentality imo

[zenith anchor]

right?

so whats confusing

even if I can't understand it knowing that the shadow would be the adjacent is good enough for me
@untold peak im sure i could help you understand the entirety of the problem-

[untold peak]

well I did end up solving it

I'm not sure if it's right so here

excuse my handwriting for being awful

@zenith anchor @humble pulsar

[humble pulsar]

169.29 what?

hotdogs? m^3 ?

[untold peak]

right sorry

teacher doesn't care about that tho

if the number you get is right he won't care

the thing that does bug me is he doesn't know computers too well and he'll get us to take pics of our work on paper and upload it

[humble pulsar]

and technically $55\tan{72^{\circ}} \approx 169.29$

[untold peak]

what is happening

I've never seen that before

[zenith anchor]

it was right

well done

[untold peak]

thank you

[somber coyote]

moshill1:

[zenith anchor]

if the angle is the sun and it's facing up at the tower then how does it make a shadow
@untold peak i just thought this was funny

[humble pulsar]

169.27*

[zenith anchor]

purely because i thought the same exact thing

when i was first learning trig application problems

[untold peak]

thank god this is almost the last of it

I've been working on re teaching myself trig all day because I can't withhold math info very well

I made a whole google doc on trig and stuff like that

also how did you get 169.27 @humble pulsar ?

[humble pulsar]

plugged in 55tan(72)

[untold peak]

that's exactly what I did

how did I not get that

no u right

I did get it wrong

I rounded up the fourth number after the decimal

that's how that happened

[upper minnow]

Can someone help

@everyone

[civic crown]

can i have help

[plain wyvern]

@civic crown @upper minnow help for what. Write the problem.

[civic crown]

this

“The measure of one acute angle of a right triangle is 6 less than twice the measure of the other acute angle. Find the measure of each acute angle.”

[dark sparrow]

what have you tried so far?

have you made a diagram?

[civic crown]

yeah

[dark sparrow]

can i see it

[civic crown]

what i got wasn’t an option tho

[dark sparrow]

what did you get and how?

also, normally angle measures are written inside the angle.

[civic crown]

oh

i got x1=48 and x2=42

[dark sparrow]

what do you mean by "x1" and "x2"

you should have had a linear equation with one solution only

[dim gyro]

So this question is it asking for “angle one is less than 90 degrees” or does it want the actual degree

[dark sparrow]

which question? 8 or 9?

also you do realize that saying "the actual degree" to refer to the size of an angle is like saying "the actual foot" to refer to a length, right

in either case, in both questions the size of angle 1 can be known exactly - and that's what the problem expects of you.

[dim gyro]

8, i mean like does it want a specific degree or does it want me to say “ angle one is equal to 90”

But u pretty much cleared it so thanks 🙏

[dark sparrow]

what do you mean by "a specific degree"?

[dim gyro]

Like “angle 1 is 78 degrees”

[upper karma]

Assuming the one side of angle of angle 1 is a diameter, it is given that angle 1 is a right angle

[dark sparrow]

i fail to see how 78 is "specific" but 90 is not

in question 8, angle 1 is 90 degrees.

[upper karma]

I need help with a trig proof

[dim gyro]

Ok, sorry im not making sense im not good at descriptions. But i mean would it want me to say “angle 1 is less than 90 degrees” or “angle 1 is 77 degrees”

Again im really sorry

[upper karma]

In a triangle ABC, where a, b, c are the opposite sides of angle A, B, and C respectively, and angle A is 60 degrees, A segment AD bisects angle A. Point D lies on BC. Prove that AD = sqrt(3)*bc/(b+c)

[dark sparrow]

did you miss some parentheses

[upper karma]

Did I?

Ah

Anyways, I can’t solve it using law of sines and it sucks

[dark sparrow]

can you show your diagram

[upper karma]

You mean the one I drew?

[dark sparrow]

yes

might make it a bit clearer what's going on

[upper karma]

Also @dim gyro angle 1 has to be 90 degrees

[dim gyro]

Yeah but I meant it like an example

[upper karma]

Oh

[dim gyro]

The 77 and 78

[upper karma]

I guess I understand

[dim gyro]

Sorry

[dark sparrow]

my current instinct is to maybe use law of cosines on ABD, ACD and ABC

this may get ugly but it might just get the job done?

not sure

[upper karma]

Ah

You could

[timid bridge]

Can sb explain to me why the functional expression of half circle is $sqrt(r^2-x^2)$? (Given that the center of the circle is (0;0))

[somber coyote]

BennyPenny:

[upper karma]

Visualize the expression, I guess

At 0, y= r

[bright hollow]

does anyone understand this?

[upper karma]

As x grows, y decreases in an arc-like fashion

At x=r and x=-r, y is 0

[bright hollow]

At x=r and x=-r, y is 0
@upper karma is that for someone else or me?

[upper karma]

For someone else

[bright hollow]

oh

will you be able to help me or u don’t have time?

[upper karma]

But the angle sum theorem states that a triangle’s exterior angles add up to 180

*interior

[bright hollow]

so should i state that as the answer?

[upper karma]

Don’t state that as the answer

[bright hollow]

cos i’m just confused on what i should on the question

[upper karma]

Use the definition of a linear pair and alternate interior angles

[bright hollow]

how can i explain that in a form of an answer? cos i can’t just write that correct ?

[upper karma]

So do you want me to answer the question for you?

[bright hollow]

if possible that can be great but if your busy or just don’t feel like it that’s fine too

[upper karma]

I’ll write a proof but it’s likely the theorems they ask you to use differ from what I know so you’ll have to fill in the reasons yourself

[bright hollow]

alright that’s great too

[upper karma]

Lines AB and CB are parallel. Angle CAD is congruent to angle ACB by the definition of alternate interior angles. Likewise, angle CBA is congruent to angle BAG

Angle BAC plus angle BAG plus angle CAD equals 180 by the definition of a linear pair

[bright hollow]

thank you so much man

[upper karma]

Through substitution, angle BAC plus angle CBA plus angle ACB

[bright hollow]

i really appreciate it

[upper karma]

=180

Oh

I wrote ACD instead of ACB there

[upper karma]

Anyone know how I can do this?

[plain wyvern]

don't know if this suits you, but a direct solution can be find through integrating

Take the point where the three circles intersect as the origin and pass a vertical straight line through it which passes through the centre of A that will be the y axis

[upper karma]

Is there a way this can be done without calculus? @plain wyvern

[plain wyvern]

Ah! I just said that in passing. You don't need integration for this at all, it's pointless

don't mind that

as for the other way, first find the white area b/w the semi-circle and circle, you can make a triangle from the centre of B and then subtract it from area of a quadrant, you get half the white area. I think you can do after that

[upper karma]

I don’t understand

What do you mean by subtract from the area of a quadrant

[vital coral]

https://i.imgur.com/aqjxDuw.png Subtract area of triangle ADE from the area of sector ADE. That gives you half the area of the white bit.

[upper karma]

OHH Thanks

[upper karma]

Anyone here

wanna help me with some area?

My teacher gave me this

Said solve the area of this

and i have zero i mean zero clue how to do this

[vital coral]

https://i.imgur.com/vhTke4M.png AC is given to be 9. And OC is the radius and so is OB. You can use trigonometry in triangle BOA to find the angle BOC and then the area of the sector OBC. Of course all this is assuming the arc CB of the extra bit is part of the same circle as the figure seems to suggest.

[upper karma]

Okay thanks il try

[upper karma]

I Don't Understand triangle congruence At All Can Someone Help Please

[dark sparrow]

is there a problem rn that you're stuck on?

[upper karma]

Yes

[dark sparrow]

ok, can i see?

[upper karma]

Let me Pull It Up

[stuck dragon]

which ones do u need help

or all

[upper karma]

All I Don't Understand This

[dark sparrow]

ok so

[stuck dragon]

u see that line going throw the 2 triangles?

through*

[upper karma]

YEs

[stuck dragon]

they share that side

[upper karma]

On D

[dark sparrow]

fallen i would appreciate not being interrupted

[stuck dragon]

oh ok

i'll let u talk

[dark sparrow]

okay so @upper karma before we start these problems, do you know what it means for two triangles to be congruent in general?

[upper karma]

I Think It Means For Them To Be The Same

[dark sparrow]

is there any reason why you're Capitalizing Every Single Word by the way

[upper karma]

No Just A Habit

[dark sparrow]

k

but yes, informally congruence means having the same size and shape

[upper karma]

Ok

But I Don't Understand How To Figure Out SAS ASA Etc

[dark sparrow]

there are a few rules for triangles specifically which let you conclude the congruence of two triangles from the fact that certain combinations of their elements match up

(i say "element" here to mean a side length or an angle measure)

the abbreviations are a concise description of the matching elements:
for example, if you have two triangles with three pairs of matching side lengths between them, you know they're congruent.

SSS means Side-Side-Side, which denotes the "three sides matching" i just talked about.

SAS means Side-Angle-Side, or in other words two sides and an angle between them

ASA means Angle-Side-Angle, two angles and a side between them

AAS means Angle-Angle-Side, or two angles and a side not between them

does that all make sense to you?

[upper karma]

Kinda

[dark sparrow]

ok which part does not make sense

[upper karma]

SAS

Wait Nvm

I Get It

[dark sparrow]

ok

so coming back to your problems

[dark sparrow]

there are two ways a pair of elements in two triangles can be matched: they can be marked as equal (with hatch marks, like sides ZW and ZS in exercise a) or they can be the same element actually common to both triangles (such as side BD in exercise c)

for example, in exercise a, looking at the diagram you see this: ZW = ZS (marked), DW = DS (marked), ZD = ZD (shared)

three matching sides

therefore the triangles can be proven congruent by SSS

[upper karma]

Wait Isn't ZD An Angle?

[dark sparrow]

why would ZD be an angle?

angles are never specified using two points.

[upper karma]

Wait How Are They Specified Then?

OHHHHHH

THE LINES HAVE ALMOST NOTHING TO DO WITH ANGLES

[dark sparrow]

three points usually

or one point, if the point in question only has one obviously-drawn angle originating at it

[upper karma]

i got 30

can someone tell me if thats right?

[stuck dragon]

yeah thats correct

[upper karma]

ah tyy

and this one

i got x =12

[stuck dragon]

yeah thats correct

[upper karma]

Ok So Can We Move On To B @dark sparrow

[dark sparrow]

sure

[upper karma]

ty

[dark sparrow]

in part b we have one pair of marked matching sides and one shared side

nothing else, really, no matter how the diagram may appear

two elements isn't enough to conclude congruence

so we can't prove these triangles congruent just from the info it gives us

[upper karma]

So If There's Only 1 Mark/Angle It's None

i got 20

[stuck dragon]

yeah thats correct

[upper karma]

kk

@dark sparrow So If There's Only 1 Mark/Angle It's None?

[dark sparrow]

yeah i guess it's impossible for two elements to be shared

keep in mind though that just because there's more than one mark doesn't automatically mean you have congruence

[upper karma]

Ok So What About C

I Think It's ASA

[dark sparrow]

no, the shared side is not between the matching angles

[upper karma]

Explain If You Could?

[dark sparrow]

the shared side is BD

do you not see how it is not between angles BAD and DBA

[upper karma]

So To Be ASA There Can't Be A Shared Side

[dark sparrow]

what? no

you're jumping to conclusions, and this time you jumped to a false one

[upper karma]

Sorry

[dark sparrow]

you should go re-read and understand what i have said about these congruence rules

[upper karma]

Alright

[upper karma]

Hello

I need help

[dark sparrow]

this person left the server just now ^

[upper karma]

[umbral snow]

[dark sparrow]

honestly better for me cause their nick is a pain

tspdsld what is this even supposed to mean

[upper karma]

true how do you even ping them

[umbral snow]

@ЦПDΣΛD#7604

You're right I can't

[upper karma]

noob

[upper karma]

The Answer Is Not Congruient Right

What does the question ask for?

Cna you post the entire problem

Because B is clear but A is not

Ignore What I Put In It's What I Think The Answers Are

For A You Have To Put If It's SSS ASA AAS Etc

[silent plank]

consider some basic geo properties

[upper karma]

?

But Did I Get 10-12 Right

[silent plank]

10 and 12 are wrong

[upper karma]

I See What I Did Wrong For 10 What's Wrong With 12

[silent plank]

consider some basic geo properties

you can deduce some additional info from the diagram

[upper karma]

Yeah The Intersect Point Will Make A Vertical Angle

OHHHHHHHH

IT'S AAS

Right?

[silent plank]

yes

[upper karma]

And Then It's The Same Thing For 10

[silent plank]

yes

[upper karma]

Thank You SO Much

[mellow sand]

I was given the information in green and had to find the yellow arc RT. I said it was 40 degrees because of Thales's theorem but that was wrong. I did 180-90-50 which gave me 40.

angle RTS is 90 given Thales's theorem

[silent plank]

arcRT would have the same measure as the central angle it subtends

(NOT the angle at the circumference which you found to be 40°)

[mellow sand]

got you

but how would you find the central angle given the information

all you know is the 50 degrees

[silent plank]

angle chasing

Thales theorem in combo with inscribed angle

after getting <RST, getting <ROT is just 1 step away

[mellow sand]

I think i can do it but differently then how you said

<R0T = 80 because <0RT and <RT0 = 50

[silent plank]

there can be multiple routes to reach the solution

[mellow sand]

so arc RT = 80

[silent plank]

yes that will work too

[mellow sand]

but continue how you would do it because im not following that

[silent plank]

look up inscribed angle theorem

[mellow sand]

<ABC = 1/2 arc AC

[silent plank]

(where B is at the circumference)

hence arcAC is 2<ABC,
or in your case:
arcRT = 2 <RST = 2*40°

[mellow sand]

ooooh

I see it now

[silent plank]

I mentioned this route because you had already found the angle at the circumference

and was to address you were stating the wrong measure
but yeh, isosceles triangle is quite efficient

[mellow sand]

I got it now, thank you

[upper karma]

anyone know how to do this?

[silent plank]

yes

[upper karma]

can you tell me how please?

[silent plank]

did you try anything yet?

[upper karma]

not really i got c = -14? we never really did this stuff

[silent plank]

how are you getting c= -14,
also what is your c supposed to represent?

[upper karma]

28-2x
/-2
=x=-14?

also C is an angle of the triangle

[silent plank]

there's a difference between c and C,
also your setup is nonsensical

it's seems like you're trying to equate <C to 0 for some reason

you should be applying the angle sum of a triangle

and solve for x

[upper karma]

so how do i do that?

[silent plank]

what's the sum of the angles in a triangle?

[upper karma]

180

[silent plank]

° and what are the sizes of your 3 sngles

[upper karma]

so to get X i would combine the X's combine the whole numbers and take away the whole number from 180 and divide by the X's right?

idk the sides of the 3 angles

[silent plank]

sizes

you are told what they are in terms of x

m<A = ...
etc

[upper karma]

m<A= 9x-7

[silent plank]

you are given the measures and sizes of all 3 angles in terms of x
their sum is 180°

[upper karma]

yea

x=12

so A= 101?

[silent plank]

yes

[upper karma]

so how do i find sides from angles?

[silent plank]

you do t have to explicitly find the sides

don't

longer sides will be opposite larger angles

eg if A is the largest angle in the triangle, side a or BC will be the longest side

[upper karma]

ohhhh

i get it now 😄

thank you

[upper karma]

can someone help me i have the problem 3 +- sqaure root of 115 all divided by 2 how do i get my roots for a graph from that

[silent plank]

what's $\frac{3\pm\sqrt{115}}{2}$ supposed to be?

[somber coyote]

ramonov:

[upper karma]

yes thats the problem

i need 2 roots from that but how do i get it

[silent plank]

do you have the exact wording of the problem?

[upper karma]

well here ill show you the whole problem i solved it down to there give me a sec

can you help me with this when your done helping synx please?

Solve each equation by using the quadratic formula. the problem is t^2-3t-28=0 and i used the formula -b-4ac to get there

[silent plank]

um what

-b-4ac is not a formula

[upper karma]

my teacher said to use b^2-4ac sorry wrote it wrong

[silent plank]

still not a formula

[upper karma]

yes it is...

maybe you will reconize this x= -b+- square root b^2-4ac/2

[silent plank]

that actually resembles a formula (ignoring the horrid typesetting)

in your case:

$\red{ t = } \frac{ 3 \pm \sqrt{9+4\cdot 28}}{2}$

[upper karma]

....

[somber coyote]

ramonov:

[silent plank]

the thing under the square root isn't 115 either

[upper karma]

yup just relized i did it wrong but the 9 is -9

[silent plank]

but that expression you reached as the t indicates represent the roots for that equation

[upper karma]

ok so i just neeed so simplify it correct?

[silent plank]

yes

[upper karma]

ahhh thanks man

ramonov do you know how to do this?

$\frac{3\pm\sqrt{106}}{2}$

[somber coyote]

Synx.is.a.qt:

[upper karma]

so thats what i get

[silent plank]

how are you getting 106

[upper karma]

oh wait hold on that was the wrong one

[silent plank]

it should be odd

[upper karma]

hold on give me one sec

$\frac{3\pm\sqrt{121}}{2}$

thats what is should be if im not wrong

[silent plank]

**t = **
yes

[somber coyote]

Synx.is.a.qt:

[silent plank]

yes

[somber coyote]

Synx.is.a.qt:

[upper karma]

so in the answer key my teacher gets t=7 and t=-4 how does she simplify from there to get those

btw thank you so much for helping me

[silent plank]

$t = \frac{3 \pm 11}{2}$ indicates: \
$t = \frac{3 + 11}{2}$ or $t = \frac{3 - 11}{2}$

[somber coyote]

ramonov:

[upper karma]

ohhhhhhh

got it THANK YOU!!!

[dense crypt]

My teacher gave us no instruction and im unsure of how to do this. What do i do?

[silent plank]

justify / give reasoning for each statement on the left

[dense crypt]

Oof that shouldve been an obvious observation. Thank you

[upper karma]

Can someone tel me my error

The answers is 121 with 2 real roots and the 2 points are -3/2 and 1/3

..

In quadratic equations, you assign the letter A to the variable with the highest power

And typically equations are written with the highest power in front and then the second-highest and so on

Ya but a is correct the highest value is 3

The highest power

Oh

Which in this case would be m^2

So that would be -6^2

And then how about B and C then

?

I do not know

Ok

If you’re asking for how to obtain $\frac{3\pm 11{2}$

[somber coyote]

Second Mikey:
Compile Error! Click the reaction for details. (You may edit your message)

[upper karma]

Then you shouldn’t be able to get that with your equation

Ah

You aren’t