#geometry-and-trigonometry

1 messages ยท Page 332 of 1

tender prawn
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this is a joke right

silk patio
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Stop harassing me

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I will report you

upper karma
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If I draw a square and put the diagonal between the center of each circle, then the radius is not applicable, right? I'm still not sure how this will work

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<@&268886789983436800> help please

buoyant tapir
silk patio
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@upper karma you join the centres up

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To make a right triangle

upper karma
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ah I see

umbral snow
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This channel is doing real well

silk patio
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The length of the hypot is R+r

green tree
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yo guys im struggling

buoyant tapir
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I rly need help on that one

tender prawn
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oh bruh im so dumb

green tree
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yes

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i tried everything

tender prawn
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ok what have you tried

green tree
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i found TC couldn't figure the rest out

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TC = AT

tender prawn
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what do you know about the relationship between ft and at

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wait nvm

upper karma
green tree
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@tender prawn so /

tender prawn
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wat

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draw the lines from f to a b c

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what is fb congruent to

upper karma
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chicken602, do you know what I should do?

tender prawn
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uh lemme take a look

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a not so elegant way would be using geometric sequence

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hold on

green tree
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yo guys i need h elp again

main meadow
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Im so confused

tender prawn
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bruh at least think about it before asking

main meadow
green tree
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bro

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ive been thinking for 50 minutes

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i cant understand this anymore

tender prawn
main meadow
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Shaded

tender prawn
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area of shaded region isn't 9 pi btw

main meadow
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Oh

tender prawn
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area of shaded is whole circle - white circle (4pi)

main meadow
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Its 5

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Yeah

tender prawn
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yeah

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wait what're the answer choices

main meadow
tender prawn
main meadow
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What is it

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@tender prawn

upper karma
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is big R for the big circle or small?

main meadow
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V

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B

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Big

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Circle

tender prawn
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oh im dumb lol

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what's the total region

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like u have shaded/total

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what's the total

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u know shaded is 5pi

main meadow
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Its5/9

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Cuz the total is 9pi

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And its asking for the shaded

tender prawn
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mhm

main meadow
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So 9-4=5

tender prawn
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5/9 should be the correct answer

main meadow
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5/9

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Yeah

main meadow
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@tender prawn

tender prawn
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label the sides and do some pythagorean theorem

main meadow
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Can u help me

tender prawn
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im not gonna tell u the answer

main meadow
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No but help me

tender prawn
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label the sides you currently have

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and what tool do you have relating to right triangles

main meadow
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So

tender prawn
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um

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are you sure

main meadow
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Idk

tender prawn
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write down the side lengths you currently have on the diagram

main meadow
tender prawn
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mhm

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so using the pythagorean theorem

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which length can you find next?

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currently there are two unknown side lengths

main meadow
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Idk

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Yes

tender prawn
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AC and AD

main meadow
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AD

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C-D is 2

tender prawn
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well to find AD you would need AC

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so how do you find AC

main meadow
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Ok

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So 2^2+1^2=c2

tender prawn
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mhm

main meadow
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So

tender prawn
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what is c

main meadow
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2+rad(1)=c

tender prawn
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wat

main meadow
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C is 2

tender prawn
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no u have 4 + 1 = (AC)^2

main meadow
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Oh

tender prawn
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so what can u do now

main meadow
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Sq root

tender prawn
main meadow
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Ok

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Then you do same?

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Answer is 3?

tender prawn
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should be

main meadow
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Ok

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Im not good with traiangles

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I mena

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Not like that

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I just didnt understand

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Im preping for the shsat

golden girder
main meadow
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Whats da

tender prawn
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idk how proper of a solution u need but u can like

main meadow
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What

golden girder
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can anyone 104.I

main meadow
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Is fhat

tender prawn
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look at the case where it's a square because it deosn't specify what parallelogram it is

golden girder
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help*

main meadow
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Make fullscreeb pls

golden girder
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it is maximum size

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all text are seen

upper karma
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Looks tough

main meadow
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Is nick lord ur prof

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@golden girder

upper karma
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You should hide that part lol

main meadow
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Lol

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Its his prof

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Maybe?

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Im not tryna be stalky

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I am just curios

golden girder
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actually it is not my question

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i do it for my friend

tender prawn
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kekw

golden girder
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maybe nick lord is his prof

golden girder
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there is not anything illegal ๐Ÿ™‚

tender prawn
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its just for your own safety

upper karma
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Those problems are hard holy

golden girder
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i was trying for 2hours

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i am a bit confused i think maybe there is some easy way i dont know

upper karma
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Anyway the ratio between areas most certainly is invariant so just let the parallelogram be a square

tender prawn
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^

upper karma
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It will probably get you the answer

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But it's not a solid proof

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Unfortunately

golden girder
tender prawn
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no

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its just asking for a solution

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it doesn't specify what type of parallelogram so you can solve it for the case where it's a square and get the answer

golden girder
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okay

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i retry

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thanks in advance

upper karma
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The intended method involves sum and difference of triangles whose areas are fractions of the parallelogram's

tender prawn
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sorry its messy

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basically i have A+B+C=pi

upper karma
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What is your goal?

tender prawn
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and the second line

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im supposed to prove the second line

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ok elmme send the problem

upper karma
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I see

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Sum to product identities

tender prawn
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oh

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ok ill take a look at that

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did i mess up my work i feel like i did

silk patio
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You know you can do it with a single picture

tender prawn
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like on a unit circle

silk patio
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Yeah, consider a triangle with those angles

tender prawn
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oh

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bruh

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a right triangle

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or any triangle

silk patio
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It has to have those angles

tender prawn
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o yea

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ok thx

silk patio
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Are you practicing for an Olympiad?

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So the area can be found in 2 ways

tender prawn
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not in particular no

silk patio
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R^2[sin(2a)+sin(2b)+sin(2c)]

tender prawn
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1/2 ab sinC and 2R^2 sinA sinB sinC?

silk patio
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Yeah with a half

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Let me draw it tho

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Cause thatโ€™s not quite careful enough

tender prawn
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ok

silk patio
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Look at the three centre triangles

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Area (1/2)R^2sin(2a)

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Or you can do the whole triangle in one go using the extended sine rule

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(1/2)xysin(a) where x=2Rsin(b) and y=2Rsin(c)

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So if you equate you get the formula

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There is always an easy way to do things

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Think smart not hard

tender prawn
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ahh okay

upper karma
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y=50 and x=80?

jagged basalt
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yep

upper karma
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kk

jagged basalt
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is this a olympics question?

upper karma
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hm?

jagged basalt
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can you solve this ?

upper karma
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i cant understand anything

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i dont know what language that is

jagged basalt
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you do not need to understand anything. it is writing values โ€‹โ€‹cd cember

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there is half circle

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you can understand br: cm

surreal sleet
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can someone help me

buoyant karma
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<@&286206848099549185>

valid osprey
surreal sleet
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congruent

valid osprey
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so they;'ve said

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twice?

surreal sleet
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if they are conqruent

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they are equal

valid osprey
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thats a weird ass question

upper karma
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I've tried everything I know of, so I am restorting to here

tender prawn
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x in what

upper karma
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I sent an image, do you see it?

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sin^2(t) = (x+3)^2 / 2

tender prawn
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yeah

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whats the question

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oh

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solve for x

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oh

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multiply by two and take sqrt of both sides probably

upper karma
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I would do that, but that doesn't give me the answer I'm looking for.

unique marten
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heeeeeeelepp

tender prawn
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or u can do the whole shift thing

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its probably d

upper karma
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It is D

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X > 1 and Y > 4

arctic mirage
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hey can someone help

mortal mason
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is the way I drew the angles for this triangle true?

upper karma
fathom root
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help pls

tawdry ruin
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@knotty merlin

jaunty marsh
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$x(36+x)=60^2$

somber coyoteBOT
jaunty marsh
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By the power of a point theorem

opal forge
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Anyone here god tier at trig?

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Like elite lol

zenith garnet
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how do i solve this?

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i feel like I'm missing something but idk

silent plank
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what's the actual question

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i see a statement,
two triangles with markings and a blue pip
what's there to solve?

eager ocean
upper karma
upper karma
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Im confused with all of these

silent plank
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what's the source

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of your confusion

upper karma
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Like im sure what im meant to put for them

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Or how to know which to put

silent plank
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the justification for congruence if it exists

upper karma
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are these all of them?

silent plank
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yes

upper karma
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so for #2 it would be none?

silent plank
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yes

upper karma
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then MNP would be congruent to

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QRP?

silent plank
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if the answer to the first part is NONE

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there would be no congruence

upper karma
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ohh

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makes sense

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for #3

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MNP congru to MQP/

sleek dove
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I need help

alpine niche
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Hi, how can I know the direction of the following normalised vector? [0.7 -0.7]

sleek dove
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Wait t/c?

thorny lintel
silent plank
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know properties of the sine function and/or unit circle

thorny lintel
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how would i start the question

upper karma
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if you're familiar with the unit circle you'd know that sin(x) = 0 when x is a multiple of 180. Find all multiples of 180 that are less or equal to* than 720 degrees*

green osprey
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hey

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i have a math question

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In parallelogram QRST if TU=18 find TR.

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can someone pls help

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<@&286206848099549185>

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anyone pls

upper karma
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ok so if TU = 18, then that must mean that RU also equals 18, yes?

green osprey
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yeah

upper karma
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so find tr from there

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segment addition

green osprey
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oh

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36?

upper karma
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๐Ÿ‘

green osprey
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ty

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i got 13,-11

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am i right

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this hw is kinda hard

stuck dragon
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what type of quadrilateral is that

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parallelogram?

green osprey
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parallelogram

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ye

stuck dragon
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ah

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i'll check

green osprey
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wouldnt 15=2x+y

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and 17=3x+2y

stuck dragon
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yeah

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yeah i got x=13 y=-11

thorny lintel
upper karma
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,rotate

somber coyoteBOT
upper karma
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@thorny lintel do you know in which quadrants tan(x) is negative?

thorny lintel
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@upper karma quadrant IV and II

upper karma
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right, and are you allowed to use a calculator to solve this problem?

thorny lintel
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yes

upper karma
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okay, so you'd do arctan(-1.428) and you should get about -55* for that

thorny lintel
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whatโ€™s arctan?

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would -55 be the only answer?

upper karma
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the inverse function of tan

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also known as $\tan^{-1}

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$\tan^{-1}

thorny lintel
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so -55 would be the only value?

upper karma
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no

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remember that you need all values within the domain of [90, 270]

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and for tan to be negative, it needs to be in the second and fourth quadrants. So you need to find the reference angles in quadrants II and IV

thorny lintel
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oh so -55 is just an angle

upper karma
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yes, put you can't use -55 because it's not in the domain [90, 270]

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Do you know how to find the reference angle?

thorny lintel
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i have some knowledge of it but not in depth

upper karma
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can you find the reference angle of 55 in the second quadrant?

thorny lintel
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would it just be 55?

upper karma
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no

thorny lintel
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oh iโ€™m not sure then

upper karma
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so the value of the angle MUST be in quadrant 2 or quadrant 3. because
Quad 1: 0-90
Quad 2: 90-180
Quad 3: 180-270
Quad 4: 270-360
and your sheet says to find an angle between 90 and 270. Do you now understand why 55 wouldn't work?

thorny lintel
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yes

green osprey
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after you guys are done can i get a bit of help

arctic cobalt
green osprey
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i know im stupid but does this work

thorny lintel
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@upper karma wait so how would arctan help?

upper karma
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since tan is positive in quadrant 3, that restricts the value of the angle to quadrant 2 (where tan is negative). To find the reference angle in quadrant 2, we just do 180 - 55 = 125. We can check our work by doing tan(125) and seeing that our answer is indeed -1.42 @thorny lintel

arctic cobalt
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How did you write that in the calculator

green osprey
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now can someone pls help

arctic cobalt
#

Yeah thatโ€™s actually right thx

upper karma
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arctan will give us the angle

green osprey
upper karma
#

the value of x

green osprey
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The diagonals are perpendicular.
The diagonals bisect each other.
One diagonal bisects the opposite angles.
One pair of opposite angles are congruent.

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pls help

thorny lintel
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ooh ok thank you @upper karma

upper karma
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np

green osprey
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;-;

upper karma
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we know that they bisect each other, right?

green osprey
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they do

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yeah i guess

upper karma
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of course they do, we can see it. so that leaves only 3 other answers

green osprey
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oh

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ok

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b and d are congruent

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so two

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i have a hunch on b

upper karma
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we also know that the diagonals are perpendicular

green osprey
#

yeah

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so is it b?

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its not a c or d

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holup

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how is b crossed out

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ac bisecs db?

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wait

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probably

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eni meeni mini moe catch a tiger by its toe if it hollers let it go eeni meeni minne moe

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oh lol

upper karma
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I mean this one: The diagonals bisect each other.

green osprey
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oh ok

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thats what i thought lol

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wait

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are the diagnols perpendicular in rectangles

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no right

upper karma
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Remember that a square is a rectangle, so all rectangles except squares do not have perpendicular diagonals.

silent plank
#

what's the actual question

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there is no proper question posted

valid osprey
#

lmaqoo

silent plank
#

@zenith garnet

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๐Ÿ‘ป

valid osprey
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LMAO tf is that

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๐Ÿ‘ป

upper karma
#

To do what

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What's the question

upper karma
#

num = 1 + e^(ia)

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denominator is quite similar

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@upper karma

upper karma
jagged magnet
#

Yo

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For number 42

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Would it be

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16 or 24

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Since

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AY is 8

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Y to z

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Should be 16 or 24

upper karma
#

ping me if you respond. Please help me with this.

lilac stag
#

help my friend needs help and idk how to do it

mint verge
#

can you guys help me with this?

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i dont know what to do sadcat sadcat sadcat

lofty inlet
#

hey can someone help me with this geometry word problem?

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Daniel installed his own 38- foot fladpole. He added a wire with one end attached to the top of the pole and the other end attached to the ground 12 feet from the base of the pole. How long was this wire?

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@here

upper karma
valid osprey
#

u could do pythagoras for each side

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or count the squares ig

upper karma
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maybe proving AB is parallel to DC and perpendicular to AD and BC (so quadrilateral becomes a rectangle), then pythagoras to show AB = BC (from a rectangle to square)

valid osprey
upper karma
valid osprey
#

how did u get x-1

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for the first one?

upper karma
valid osprey
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yeah im saying do that for every side

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ohhhhhhhhhhhhhhhhhhhhhhh

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ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

upper karma
#

still not enough

valid osprey
#

ahhhhhhhhhhhhhhhhhhhhhhhh

upper karma
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Iโ€™m very confused about this but it could also be y=x-2. I just need help with these three

valid osprey
#

so for the first one

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if its being enlarged by a scale factor of 1/3

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y = x - 3

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enlarged by 1/3

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what do u think we have to do

umbral snow
#

@upper karma
Instead, check every angle is 90ยฐ

valid osprey
#

๐Ÿ˜ฎ

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nva thoughta dax

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actually

upper karma
#

alr

valid osprey
#

its says centred at the originx

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how do we factor that into our calcs if we dont know the original position of the shape

upper karma
#

Bro can you tell me how to do it. If you canโ€™t itโ€™s fine Iโ€™m just confused and need someone to help.

umbral snow
#

@upper karma
Or wait, my suggestion is stupid. Every side has the same length, and opposite sides are parallel is easier

valid osprey
#

these questions are quite odd

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or i might be doing them wrong

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to englarge them i did multiply them

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but then

upper karma
#

Thatโ€™s what I got for the first one mate

valid osprey
#

yeah

upper karma
#

Itโ€™s one question but the rest is what you apply for each graph

valid osprey
#

wait hold on

upper karma
#

yeah I got an error on that

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thanks

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Like y=x-3 is the equation that is dilated by and is used for questions 1,2,3

valid osprey
#

yes

upper karma
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So Iโ€™m confused on what to do in 2 and 3 since the equation y=x-3 had multiple coordination

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Coordinates*

valid osprey
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a coordinate is one point

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a line has many points

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they are saying that u need to enlarge the whole line by that scale factor

upper karma
#

So question 2. Has a scale factor of 2 and centered at the origin

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Man anyone? This is due in 15 mins

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Itโ€™s okay if you canโ€™t just say it Iโ€™ll just do what I can

valid osprey
#

just multiply by 2

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like u did at with number 1

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but they said the scale factor is 1/3

upper karma
#

I didnโ€™t multiply for the first I cut it down by 1/3 since itโ€™s dilated

valid osprey
#

cut it down

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dilated basically mean to enlarge

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the scale factor is 1/3

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so u multiplied the equation of the line (x - 3) by 1/3

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so for the second one

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just multiply it by 2

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have u guys not studied enlargements

upper karma
#

What? So multiply (x-3)*2 and no just got these three pwctice wiestikns today

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Practice questions*

valid osprey
#

yes multiply it by 2

upper karma
#

Got 2x-6..........

valid osprey
#

yeah

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is that not the answer?

upper karma
#

Tf idk you probably know this better than me

valid osprey
#

i was just asking bc i thought u also had the answers

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do u understand why we multiplied by 2

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its the same as Q1

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u multiplied by 1/3

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bc that was the scale factor

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does that make sense?

upper karma
#

Yeah scale factor is dilated so for 3 it would be the centered coordinate and scale factor also multiplied by 2?

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But (-1,-2) is the center now but it would still be the same the same again?

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Due in 5 mins now. Iโ€™ll try dis Man. Thanks for trying to help me

valid osprey
#

the centre of the shape changed

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or the line

upper karma
#

Yeah to (1,-2) for question 3

valid osprey
#

yeah

upper karma
#

So the same step?

valid osprey
#

yeah

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if they havent toild u to draw the graph, then the centre does not matter much

upper karma
#

Which is literally the same equation.

valid osprey
#

yeah

upper karma
#

Itโ€™s y=2x-2 again?

valid osprey
#

they are throwing extra info at u to confuse u

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nope

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y = 2(x - 3)

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cant br y = 2x - 2

upper karma
#

Alright Iโ€™ll just ask my teacher about this tomorrow. Like we didnโ€™t even start of by learning just practicing

valid osprey
#

aight

upper karma
#

But thanks mate

valid osprey
#

yw

upper karma
#

Alright itโ€™s correct. But how you get y=2(x-3) when you said itโ€™s the same equation if the center is Changed?

valid osprey
#

lemme send a vid in a bit

upper karma
#

Vid? Ok

valid osprey
#

srry channelk takenb

upper karma
#

What video you sending?

umbral snow
#

Same as before @upper karma
Make sure the sides are equal length, and opposite sides are parallel

valid osprey
#

nvm about the video

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but u dont need to care about the origin

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if it says enlarge

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and they've given u an equation

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ur probably gonna study enlargements soon

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and it will all make sense

upper karma
main meadow
#

Hi

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<@&286206848099549185>

oak citrus
#

what is the formula for area of circle?

next jackal
oak citrus
#

ah

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great minds think alike

next jackal
#

clown to clown

main meadow
glacial dawn
#

use pythagoras and solve

main meadow
#

Yes

oak citrus
#

pythagoream theorem is a^2+b^2 = c^2

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so basically

main meadow
#

Opps forgot to add the ^2

oak citrus
#

the bigger issue is

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that it should be

next jackal
#

@main meadow can you point out what the hypotenuse of that triangle is?

main meadow
#

Longest sode

oak citrus
#

what is the longest side in this case?

main meadow
#

5a

oak citrus
#

and if c in this equation is the hypotenuse, would you agree that whatever a and b are they equals a^2+b^2=5a^2

main meadow
#

Teah

oak citrus
#

ok

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and what are the a & b values in this case?

main meadow
#

3a for a abd 12 for b

oak citrus
#

ok so with this knowledge can you setup the equation again?

main meadow
#

Yeah

oak citrus
#

ok do that and send

next jackal
#

@oak citrus is a man of patience, commitment and s h e e r f o c k i n g w i l l

main meadow
#

Oh is 9

oak citrus
#

?

main meadow
#

A=9

oak citrus
#

did you finish problem

main meadow
#

Yes

oak citrus
#

i havent done the problem but send work

main meadow
#

6Rad2

next jackal
#

No it's wrong

main meadow
#

6|โ€”
|2

#

Oh

oak citrus
#

send pic of your work

next jackal
#

what's rad doing in this?

main meadow
#

Mb

humble pulsar
main meadow
#

Its

#

3

#

Since rad9 is 3

#

So 3

humble pulsar
#

yes

main meadow
#

Oops i forgot to rad

oak citrus
#

rad as in sqrt?

main meadow
#

Yeah

#

Rad 9 is 3

next jackal
#

I'd suggest you call it square root instead of radical

oak citrus
#

yeah

#

agreed

#

because later on in math rad stands for radians

late breach
#

how would I know when to add the 180

humble pulsar
#

depends on what quadrant you need

#

tanx < 0 will always give an angle in quad 4

#

if the angle is in quad 2, you add pi / 180

late breach
#

ok thank you

upper karma
#

pick a postulate and then apply it

zenith garnet
#

how can i prove if this is true or false

upper karma
#

see if you can use one of the triangle theorems

zenith garnet
#

well i only know the congruence of one angle

#

and one side

#

so i cant prove anything

upper karma
#

@zenith garnet you have to prove one of the other sides or angles is congruent first

zenith garnet
#

ya thats why im confused about

#

i dont know how to do that

main meadow
tender prawn
#

ok im pretty sure ik how to do this

tender prawn
#

like sin^3 A = 8R^3 by extended law of sines

#

so i did that, top and bottom cancelled out, 8R^3=7

main meadow
#

Yes

tender prawn
#

is that correct?

main meadow
#

But no

#

The answer choices r there

tender prawn
#

whats the base whats teh height

main meadow
#

Idk

#

I got this from someone

tender prawn
#

...

#

figure it out from diagram

main meadow
#

Idk how to do it so i come out here to ask

tender prawn
#

well

#

how would you find the base

alpine niche
main meadow
tender prawn
#

extend AB and draw a line from C straight down to hit line ab

upper karma
#

or u could use heron's formula

#

Or do you have to do it a certain way

humble pulsar
#

why would you use heron's formula when you know the base and height...

upper karma
#

I did not look at the picture lmao I just looked at find area

#

If you know base and height then you're good

tender prawn
#

teacher explained in class but i wasnt paying attention :/

#

pretty sure its something to do w half angle formula

#

and maybe herons formula

#

kinda looks like law of cosines

#

hmm

#

i like multiplied both sides by s(s-a) and did herons formula and then used a=1/2bc*sinA to get

#

sinA = s(s-a)(1-cosA)

#

probably wrong direction tbh

hasty bone
#

hey can anyone help me

upper karma
silk patio
#

Similar triangles

upper karma
#

x= similar triangles?

tender prawn
#

the top triangle is similar to the whole triangle

#

and then use side lengths of similar triangles

#

i proved the second part using area of triangle = sr

#

and i think im supposed to somehow relate it to the first but idk how :/

#

kinda avoiding the half angle formula but it might be that

#

oh im dumb i turned cot into cos/sin instead of 1/tan and using tan half angle formula

tender prawn
#

ahh i finally got it lol

#

i was supposed to use the sum/difference of cot and tan

#

man trig is hard

upper karma
#

help

#

I know like 10 different ways to do this

#

but I don't know how to take up every slot

#

my teacher when she teaches it usually uses every slot

#

never has one wasted

#

but all the ways I solved it

#

didn't use them all

silent plank
#

show what you're doing

upper karma
#

ok

#

wait

#

I deleted it let me retype it

silent plank
#

wait, statement 2 doesn't even make sense

upper karma
#

that's what I mean

#

@silent plank

silent plank
#

statement 2 doesn't make sense

upper karma
#

how

#

the traversal

#

makes it true no matter what

#

wait

#

that's only if it's parallel

#

๐Ÿ‘€

silent plank
#

you can't assume that lines c and d are parallel at that stage

upper karma
#

yea

#

I just realized

silent plank
#

that statement is something you could aim to reach

upper karma
#

this guy told me that's how I should start it

silent plank
#

and then use the converse to justify that the lines are parallel

upper karma
#

so how do I start it?

#

angle 7 congruent to angle 3

#

?

#

angle 7 congruent to angle 1

#

vertical

silent plank
#

there are multiply routes you can take

#

do some angle chasing and apply a converse related to parallel lines

upper karma
#

okay

late breach
#

Can someone explain how I would know to divide these degrees by 2?

silent plank
#

DeMoirvre's

limpid gust
west basin
#

well you have (6x-7) do you know what angles on a line add up to

limpid gust
#

I solved that

#

i was being dumb

untold crow
#

i need help. i have 9-13 questions on a study guide. my test from this study guide is tomorrow. please someone help.

limpid gust
#

because of x and 6

#

y*

prime drum
#

yo ill pay someone if they help me with a couple problems

#

dm me!

west basin
#

its against the rules to pay for help

prime drum
#

oh nvm then

west basin
#

just post your problems and someone will help you

prime drum
#

could someone help me with this please!

west basin
#

sure can

#

break $sin 2\theta$ down into $2cos \theta sin \theta$

#

will that help you at all?

somber coyoteBOT
prime drum
#

nah

#

i need answers g

west basin
#

we dont give answers lol

#

just use symbolab or something if you want that

zenith garnet
#

is it possible to prove this is congruent with the info given

#

im not sure how to decide if its true or false

tepid finch
#

if its congruent every side must be equal

#

can you think of a situation where AC/BC don't necessarily equal EG/GF

slate blade
#

Congruence needs one of the following requirements:

  • SSS (Side, Side, Side)
    Basically if you know all 3 sides are equal in magnitude, they are congruent
    -SAS (Side, Angle, Side)
    If two pairs of sides are equal in length, and the included angles are equal, then the triangles are congruent, But this one needs the sides to sandwich the angle
    -ASA (Angle, Side, Angle) There's another variation of this called AAS
    Basically your two given pairs of angles are the same, and the sides are the same
    -RHS (Right angle, Hypotenuse, Side)
    For right angle triangles only
#

In your case @zenith garnet you only have 2 pieces of information in your triangles, therefore you cannot reach that conclusion that they are congruent unless I am stoopid

#

SSA is another variation (but sometimes you cannot prove congruence with it because of the ambiguous case)

#

and AAA is the only one that you legit cannot use, because that identity only demonstrates similarity, not congruence

#

hope this helps

near tendon
#

Can someone give me the steps in order to prove this trig identity? Not the greatest at Trig functions & identities

#

Please and thank you๐Ÿ‘

#

sin(2x)/1-cos(2x)= 2/sin(2x)sec^2(x)

earnest echo
#

Start from RHS
And use half angle identities on both numerator and denominator

#

Once you simplify it a bit
Use double angle to get your desired result

#

Not RHS, use LHS

near tendon
#

Start off with the Left Side instead?

earnest echo
#

Yeah

near tendon
#

errrr

slate blade
#

u get anywhere?

near tendon
#

Nah not really

slate blade
#

would u like a step through?

near tendon
#

yes please

slate blade
#

aight give me a moment let me actually solve it myself

near tendon
#

Okay thank you

#

I've only been able to change sin(2x) into 2sin(x)cos(x) -- Double Angle

earnest echo
#

Do the same for 1-cos(2x)

near tendon
#

Okay

#

so 1-2sin^2(x)

earnest echo
#

That's wrong

slate blade
#

remember there are 3 options for cos(2x)

near tendon
#

Okay yeah thats true

earnest echo
#

1- cos(2x)= 2 sinยฒ(x)

near tendon
#

Ok got it

#

thank you

slate blade
#

epic good job

winged vine
#

hey

limpid phoenix
raven heart
#

hey can1 help me with this

pure cape
#

@raven heart can you find the obtuse angle inside?

#

and you should use the property that all angles in a triangle adds up to 180 deg

raven heart
#

well how??

#

can u show me

#

@pure cape

#

hey any1....i need immediate help

pure cape
#

given angle ABC

silent plank
#

need immediate help

pure cape
#

can you find the reflex angle

#

just give me the answer to the reflex angle

raven heart
#

yeah...its 310

#

but i dont know any angle inside

pure cape
#

or how you would go about finding it

#

yep

#

so can you do that in reverse for your exercise

#

you just have to find all of the angles in your triangle

#

and add them up

#

you also know that by adding up all 3 angles, it will give you 180

hybrid solstice
#

can someone help me with that

pure cape
#

which one do you think it is?

hybrid solstice
#

i think its the second

pure cape
#

and why is that?

hybrid solstice
#

only reason why i think that is B and F will the right angles

pure cape
#

well you're almost right

#

if the statement is correct, it means that angle C and angle E are equal, and the same for B and F, A and D

#

which is true from what we see here

#

if you say its correct because B and F are equal then its wrong, because there isnt enough evidence

hybrid solstice
#

oh ok

#

ohhh

#

so then

#

the third one?

pure cape
#

no, the second is right

#

im just saying that your reasoning is wrong

hybrid solstice
#

ohh ok

#

this was pretty hard too

pure cape
#

remember the rules of congruence

#

what rule is the first one

hybrid solstice
#

SSS

pure cape
#

are you sure?

#

because as i see it, the first one only talks about a pair of sides

#

and two pairs of angles

#

rather than 3 pairs of sides

hybrid solstice
#

aas?

pure cape
#

close

#

asa

hybrid solstice
#

oh

pure cape
#

what about the second one

hybrid solstice
#

i ahve to prive wihich is wrong

pure cape
#

yes

#

so lets find which one is correct first

#

and then we shall know which one is wrong

hybrid solstice
#

ok

pure cape
#

i see 2 pairs of sides, and a pair of angles

#

is that sas?

#

pay close attention to the positioning

hybrid solstice
#

that would have to be sas

#

aas wouldnt work

pure cape
#

but is it really sas

#

i dont know.....i mean the angle isnt in the middle of the two sides

hybrid solstice
#

youre talking about the first one correct?

pure cape
#

nah

#

im talking about the second one

hybrid solstice
#

the angle is between AC and BC

#

well angle C is

pure cape
#

yes

#

so for the second one

#

to prove that the triangles are congruent,

#

we have to use angle C

#

so that means the second one is wrong

hybrid solstice
#

ohh ok

#

bec we would need more info correct

pure cape
#

yeah

hybrid solstice
#

and that info is C

pure cape
#

or AB

hybrid solstice
#

oh ok

#

thank you

slim saddle
#

Any idea of how to solve this?

#

please ping me

humble pulsar
#

@slim saddle if DEF ~ JKL, then m<D = m<J

slim saddle
#

ok

#

so 7x-12+9x-20+52=180?

humble pulsar
#

yes

slim saddle
#

thanks!

#

any clue of how to find the second one?

humble pulsar
#

which one has 2 sides and 1 angle?

slim saddle
#

2nd one?

humble pulsar
#

yes

slim saddle
#

thanks

#

it isn't the 2nd one

upper karma
#

(tan27 x tan53)/sin30

#

How to solve this ^^

silent plank
#

apply properties of the tan function

#

as well as trig functions evaluated at special angles

green osprey
#

wait

#

how am i one minute earlier

#

than you

#

wait fk im just sht at math

#

29m is less than 38m

#

anyways

#

do squares have legs like trapazoids

silent plank
#

wdym by like trapazoids?

green osprey
#

never mind

silent plank
#

squares are special trapezoids

green osprey
#

oh

thorny maple
silent plank
#

yes

thorny maple
#

4:5?

solemn axle
#

Thatโ€™s what I got

sleek dove
#

I need help

west basin
#

its a 45-45-90

#

that means the hypotenuse will be the product of leg*sqrt(2)

arctic cobalt
#

Your given the length of one of the legs which is 9 the and both of the legs are the same length the hypotenuse which is opposite to the right angle sign is equal to 9x2

umbral snow
#

Do you know the statement of the law of cosines? Have you gotten any progress in it?

arctic cobalt
#

You mean the formula

unreal vine
#

how do i find a diff restraint?

umbral snow
#

The formula, and what everything in it means

arctic cobalt
#

Yeah I get it

#

But I got 35.95 for c^2 which Iโ€™m pretty sure is wrong

umbral snow
#

xยฒ = 13ยฒ + 24ยฒ - 2(13)(24)cos(87ยฐ)

arctic cobalt
#

Is that what c is equal to?

umbral snow
#

What's c?

#

I see an x on your page

arctic cobalt
#

Yeah I mean x

umbral snow
#

That's what xยฒ is equal to anyway

arctic cobalt
#

What did you do to get that

umbral snow
#

xยฒ = 13ยฒ + 24ยฒ - 2(13)(24)cos(87ยฐ)

arctic cobalt
#

Cause I did 169 plus 576 equals 745

umbral snow
#

Which should be the law of cosines, applied to that triangle. Let me know of course if I made any mistake haha

arctic cobalt
#

The second part is confusing me what do I do with the cos 87

umbral snow
#

,w cos(87ยฐ)

arctic cobalt
#

Did you distribute -2 by 14 and 24

umbral snow
#

cos(87) is just a number, approximately 0.05234...

arctic cobalt
#

13 not 14

umbral snow
#

Everything is being multiplied, there's nothing to distribute

#

So you have the right idea, do every term separately then add them all up in the end

arctic cobalt
#

So what do I do with the negative 2 the 13 and the 34 left over

umbral snow
#

The last term is just
2(13)(24)(0.0523359...)

arctic cobalt
#

So -26 times 24 time 0.05

umbral snow
#

Approximately

arctic cobalt
#

I got it now thank you

humble pulsar
#

@molten bronze cant help w/o the question

humble pulsar
#

Can't help w/o the question

glacial dawn
#

Well the first is a given right?

upper karma
molten bronze
west basin
#

post your question

molten bronze
#

Ohh thank you so much

#

What are the blanks @west basin

#
  1. given 2) bd=bd 3) ???
#

Sas or hl

west basin
#

should be sas

#

since they share an angle between two shared sides

molten bronze
#

Yea I just realized

#

The angle doesnโ€™t show 90 degrees to

#

Can I ask one more ?

#
  1. pa =ya 3) segment bisector or reflective property?
#

Idk which

west basin
#

reflexive

#

its better to use that than bisector

molten bronze
#

Itโ€™s a multiple choice and they have both tbh

west basin
#

well youd also need to prove its a bisector if you were doing that

molten bronze
#

Ohhh I guess midpoint isnโ€™t bisecting py

#

Itโ€™s a point

#

Just a point I presume

#

So then it has to be reflexive property

#

What would 4 be in that case? Sss still right

west basin
#

actually you could use bisector i think

#

because it gives you the midpoint

#

i didnt read that

molten bronze
#

Ahhh so confused

#

Uhh

#

I think itโ€™s reflexive still

#

Cause I feel like with midpoint it canโ€™t bisect

west basin
#

yeah because they both share LA

#

just go with reflexive

molten bronze
#

Okay, I have one more

#

This is my last concern

#

What are the blanks for this one :?

#

Just wanna make sure I did it right

west basin
#

what did you put?

molten bronze
#
  1. definition of midpoint
#

Statement 3) angle aix = angle oim

#

Reason 3 vertical angles

#
  1. Sas
west basin
#

looks good to me

molten bronze
#

Thanks ๐Ÿ™‚

upper karma
upper karma
#

help

upper karma
#

bruh

tender prawn
#

just use a bunch of supp and corresponding angles

steep dawn
#

what's a linear pair

#

for 2 if you're using that as proof you need a few more lines

#

@upper karma

upper karma
#

uh

upper karma
plain wyvern
#

@upper karma

#

also this is the wrong channel for this question

elder creek
#

i need help lol

polar summit
#

put problems 1 by 1

placid bone
#

lmao theres no question there????

upper karma
#

if everytime you try to make a circle with a compass it makes a spiral is that user error or a bad compass?

earnest echo
#

Probably user error

#

Or the screw could be lose