geometry-and-trigonometry

[wintry loom]

there are tons of great resources across the internet

admittedly i can only name those twoo off the top of my head but still

[quaint oasis]

Ok- my teacher is bad so is there like a youtuber or-

Ah

[quaint oasis]

Better than nothing🤷

Well thanks

[wintry loom]

you're free to search for one! tons of material on yt, pick whatever works for you

but yeah, good luck

[quaint oasis]

Ok, thanks a lot

[quaint oasis]

Yeah, I will defientlt make sure to us these.

[leaden dew]

hello guys

I dont get this,

I dont see -2 on the graph

its -6 but i dont get how it's -6

So this was the answer but i dont get how

[silver roost]

The space between 0 and -5 has 4 divisions

The second one from the right would be -2

[leaden dew]

I got another one, so id be finding the space between it? @silver roost

[silver roost]

In that case there are 2 divisions between 0 and -3

Which correspond to -1 and -2

Think of it like a ruler with the millimeter divisions unmarked

[leaden dew]

can you draw it out? i dont really get it sorry

im a visual learner

@silver roost

[silver roost]

It's basically a number line with some numbers unmarked

[leaden dew]

where the heck did the -2 come from?

i get the -1 not the -2

[silver roost]

-2 is between -1 and -3

[leaden dew]

okay how does that relate to whats on the line though?

[silver roost]

There are 2 unmarked divisions between 0 and -3

Since there are only 2 numbers between 0 and -3, we can just say that those divisions correspond to -1 and -2

[leaden dew]

uhhh

[silent crystal]

I already

Did that part

I ment the relationship between 18x+9 and 3y

[ancient kindle]

well the angle next to 18x+9 is 3y

that's what i was trying to imply

18x + 9 equals 117, and 117 + 3y equals 180, so 18x+9 + 3y = 180

[silent crystal]

I was gonna do that

But I second guessed

Myself

[leaden dew]

i get it now

omg theres another question with even a bigger number line

[silent crystal]

So then x= 6

And y= 21

Then

@ancient kindle thank you, smart man, your explanation helped me through the whole problem

[silent crystal]

What are the different types of angles besides corresponding and consecutive interior and exterior and alternate exterior and all the stuff, this is a sample SAT geometry question which I couldn’t get because of the angels being weird but Geometry is where I struggle

[ionic coral]

anyone willing to teach me basic trigo

<@&286206848099549185>

hi

do u know about angle of elevation and depression

[ionic coral]

<@&286206848099549185>

[obsidian cradle]

can you send a photo

[ionic coral]

@obsidian cradle

[obsidian cradle]

ohhh shoot

i remember this

[ionic coral]

is it hard

i know how to find p1 using triangle ABD but after that im lost

[obsidian cradle]

its not hard

did i forget how to do this? yes

let me learn rq

relearn*

[ionic coral]

sometimes there is only word given problem

[obsidian cradle]

draw a diagram representing the situation as a right triangle, then use the tangent function to find the angle by taking the arctangent (tan^-1) of the ratio between the "opposite" side (vertical height) and the "adjacent" side (horizontal distance); essentially, the formula is: "angle of elevation = arctan (height / distance)" where "height" is the vertical distance to the object and "distance" is the horizontal distance from the observer to the object.

[ionic coral]

idk how to make a figure

[obsidian cradle]

okay so

its basically doing tan

[ionic coral]

ok

[obsidian cradle]

yk tangent right

opposite / adj

[ionic coral]

yes

sohcahtoa

[obsidian cradle]

yup yup yup

so what has you lost after that

you have one measure

[ionic coral]

idk how to get BC p2 and h

[obsidian cradle]

which is the height of the tower right

[ionic coral]

yes

[obsidian cradle]

oh its num 1

[ionic coral]

ye

[obsidian cradle]

so to find the side

youd do tan of an angle

and then the opposite side of that angle / adjacent side no?

and that way u can find either the opposite side or adjacent

for example if the opposite side is 3m

and the angle is 48*

then u do tan48 = 3/x

and if the adjacent side is 3m

u do tan48 = x/3

and if u have both sides you just do the inverse of tan

to find theta

[ionic coral]

so if u need to find the opposite u need to use tan?

tan(10) = 180/p1

[obsidian cradle]

ya

and then u do p1 = tan(10) / 180

[ionic coral]

then p1=tan(10)180

[obsidian cradle]

make sure you're in degrees

it would be division

[ionic coral]

yes

[obsidian cradle]

u did multiplication here

[ionic coral]

what about adjacent

oh

[obsidian cradle]

if you're finding adjacent

let opposite = 3

tan(angle) = 3 / x

x * tan(angle) = 3

x = 3 / tan(angle)

so thats an example of how

youre just playing around w the x

[ionic coral]

am i suppose to divide

[obsidian cradle]

look

tan(10) = 180/p1 right

[ionic coral]

yes

[obsidian cradle]

then u multiply p1 by both sides to clear the denominator

so then u get

[ionic coral]

ohhh

[obsidian cradle]

p1 * tan(10) = 180

and then u divide both sides by tan(10)

[ionic coral]

if p1 is above i transfer?

example tan(10)= x/180

does it become x=tan(10)180?

[obsidian cradle]

yes

bc u multiply both sides by 180

[ionic coral]

ohhh

i get it now

[obsidian cradle]

yippee

[ionic coral]

now for the hard part

how do u get BC

[obsidian cradle]

okay so AB = 180ft

umm

okay so

[ionic coral]

i saw my friend did uh

subtract angle

idk how he did it

[obsidian cradle]

i dont remember

i feel like using the 180ft line

with the angle

[ionic coral]

hm

[obsidian cradle]

u create a tan equation to figure out a side in TRIANGLE ABC or DCB

and then from there youd use another equation to find the value of BC

[ionic coral]

but there is no given

on triangle DCB

only under it 42* and 34*

[obsidian cradle]

yes there is

side AB is 180ft

and then u could use that to find side DB

and then use that to find side BC

maybe

i dunno

geometry too hard

[ionic coral]

fr

i will try

[sterile isle]

Hello everyone I need help in Analytical Geometry

"The equation of the straight line given its slope and intercepted part of y-axis" concept

[obsidian harness]

@gray osprey

hint: the tangent at the point where the quarter-circle and the semicircle meet is perpendicular to both the radius of the quarter-circle, and the semicircle

same thing for the quarter-circle and the circle actually

what theorem do you use a lot in geometry questions, especially ones that involve circles?

so you can definitely set up a direct equation for the quarter-circle and the semicircle, if you call the radius of the semicircle R for example

the radius of the circle, r, will take some more work after you find R

[gray osprey]

I found it

But now l need to find the radius of the smaller circle

It’s 4/9 but idk how to explain it

[rustic rampart]

any tips for memorizing theorems for proofs

[gray osprey]

Look Say cover eye check

[rustic rampart]

now THIS is true sigma male advice

[gray osprey]

You can also try to build things like patterns to get further understanding

Like insights into why the theory works

But if you don’t know how like me look say cover eye check is the sigma way

[rustic rampart]

got it thanks

[worn stag]

Derive it and use it a lot

Over time you'll recall it pretty fast

[rustic rampart]

what if i have a test on it sayyyy in about 9 hours

[gray osprey]

This might be unconventional but take a photo on your phone and when your in the toilet outside walking look at the thereom say it in ur head try recall it then take a break

The unconventional bit is if that doesn’t work repeat everything in your head just before the test then write it down somewhere as soon as you get ur paper

[rustic rampart]

thats hardly unconventional

unconventional is like

okay well i wont get into details but thats not unconventional dw

[gray osprey]

Idk English is not my thing lol

[rustic rampart]

nah ur good

[gray osprey]

But take a photo on ur phone trust me it’ll help you

[rustic rampart]

ok bet

[gray osprey]

Also just before you go to bed and when you wake up tomorrow look at it then

[rustic rampart]

for proofs questions, especially two column proofs, is there always gonna be a set answer and order or can answers vary??

[obsidian harness]

answers can vary

[rustic rampart]

oh SIGMALICIOUS

[obsidian harness]

ok what the-

in part because despite the rigour you might assume from grade school geometry

you aren't actually given a set of axioms to work with

for instance, one text assumes SAS congruence as a given, then derives all the other forms of congruence from that

https://math.berkeley.edu/~wu/Pre-Algebra.pdf

I recommend this text

Euclid's Elements is not taught in most places anymore, for better or for worse

[obsidian harness]

I've added more of my own thoughts on this

[rustic rampart]

oh thanks

lemme read

[obsidian harness]

also in Lockhart's Lament, there's the idea that two-column proofs are presented as the only form of valid proof in geometry

when a proof could be a paragraph

or even a picture, with enough explanation

studying geometry like this can dull the mind rather than inviting you to see why certain things are true for yourself, by experimenting and hypothesising

[obsidian harness]

going back to this, it really sucks that trigonometry is taught as a separate thing, when in reality it's one interconnected whole

it stops students from making connections, such as:
SAS, SSS are cases of the cosine rule
ASA, AAS are cases of the sine rule

you can use the cosine rule to show that if two triangles are SAS, they are SSS for example (and hence congruent, if that's your definition)

[rustic rampart]

uhhh yeah im just doing geometry so idk what ur talking about rn

[obsidian harness]

my point is that mathematics isn't authoritative

you can't say 2 + 2 = 5 but there's a lot of human involvement and subjectivity as well

[rustic rampart]

oh oh okay i see

[obsidian harness]

I guess that's what makes maths beautiful

[rustic rampart]

ah yes straight Cs

so beautiful

[obsidian harness]

you have a way to check if your teacher is right or not, if they tell you something wrong

[rustic rampart]

i should do that

and rack in some extra points

[deft cedar]

Can sb help me in this task?

I made the drawing

And i know that the quadrilaterals LNDF and CMKE are similar to each other

But idk what,s next

[deft cedar]

Anyone?

[wintry loom]

https://en.wikipedia.org/wiki/Ptolemy's_theorem
found this off a quick google search. may be relevant to you

dont know how you would obtain lengths though

[upper karma]

I don’t understand trigonometric equations

[dusk venture]

I think that by applying Ptolemy's theorem the result can be achieved

[amber helm]

help me with this

no other data is given

[upper karma]

,rotate

[deft cedar]

Pleas can anyone explain me this???

Pleas

[astral onyx]

Someone know if there exist a solutions manual for shively l. Introduction to modern geometry?

[dreamy vessel]

There's not enough information; this problem is just straight up impossible

[mild sleet]

If one more angle or side length was known it will be possible via trig but we dont have that

[real girder]

A could be anywhere above or below B

[limpid marsh]

Trigonometry is so paper-consuming

[upper karma]

Wait let me think guys

[worn stag]

That's an excuse, We know you eat and chew on papers in private.

[upper karma]

I'm new here

Can i solve it here or private

?

[upper karma]

We can solve it by cosin i think

Wait let me show my idea

[worn stag]

We can't

[upper karma]

Yeah

We need more angel or side

[mild sleet]

thats what i said

[umbral wolf]

Suppose there is a circle with radius 6 cm and center point O . There is a point P located outside the circle such that the distance from P to O is 15 cm. From P, two tangent lines are drawn to the circle, touching it at points A and B. Draw chord AB inside the circle. If angle AOB = 90 degrees , what is the area of triangle ( POA )?

[upper karma]

tried anything ?

[umbral wolf]

here is what i think after drawing it ,
since PA is tangent and OA is a radius so this means OA is perpindicular to PA meaning PAO = 90 degrees,
now we have PO = 15 cm and OA = 6 CM , we can just say that PA^2 = OA^2 + OP ^2 .
now i can say that area of POA = 1/2 * OA * PA

but someone drew my attention to how can AOB be 90 degrees if PA and PB are tangents and O is the center of the circle

[upper karma]

you got the pythogoreas theorem wrong

rest of it is good

[upper karma]

why not ?

good point

[upper karma]

:p

[umbral wolf]

Yeah the whole question has a logical flaw, So i voted it unsolvable and skipped

[obsidian hornet]

(XYZ)-angle; (LND)=(DFE)=(OEB)=180-(CMK), (NLD)=(LAD)=(BCK)=(EMK), (CME)+(NFE)=180.

[deft cedar]

Can you explain more why CME+NFE=180?

@obsidian hornet

[deft cedar]

Thank you man you helped me so much

[obsidian hornet]

No problem

[acoustic snow]

How to get good at proofs

We had this proof in this class

Really difficult for me

I was able to get the first 3 or 4 steps

[obsidian harness]

which one, 1. or 2.

2. right?

[acoustic snow]

2

[obsidian harness]

what was the approach they took?

[obsidian harness]

weird, my message just disappeared

I'll have a read

[acoustic snow]

Ok

[obsidian harness]

it's too blurry

[acoustic snow]

Is jusf doing more proofs actually going to help me

And get better

Cuz idk

[obsidian harness]

help you with what

[acoustic snow]

Do better with other hard proofs

[obsidian harness]

I guess so

[acoustic snow]

And these take me so long

[obsidian harness]

yeah most proofs are like 5 lines or less

especially if this is your first year of high school or something

[acoustic snow]

This one was 10 lines

[obsidian harness]

you don't have that much experience to begin with

[acoustic snow]

It’s like the highest level math u can fake

[obsidian harness]

interesting

[acoustic snow]

So he’s making it really hard

[obsidian harness]

thought they would teach you precalc then

[acoustic snow]

No our school has acc geo trig a2 in one year

And then a2 precalc

[obsidian harness]

the approach I was thinking of was to show that angle FAB = angle FBA
which is true iff angle CAE = angle DBC

[acoustic snow]

There’s not enough info to prove that tho

[obsidian harness]

which is true iff triangles CAE = CBD by say SAS

[obsidian harness]

ohhhh okay

yeah doing trig and geo in the same year makes a ton of sense

#geometry-and-trigonometry message

[acoustic snow]

And algebra 2

[obsidian harness]

I went on a rant here btw and it's related

[obsidian harness]

when?

[acoustic snow]

O

[acoustic snow]

Second semester

[obsidian harness]

jesus all that in one year

[acoustic snow]

We finish geometry in first

And then trig is combined with Alg 2

Alg 2 is insanely fast

[obsidian harness]

you can show this though

CE = ED from the question, triangle CED is isosceles

angle DCE is shared

AC = BC from the question

and then work backwards, iff means $\iff$

[somber coyote]

south's secret twin brother

[acoustic snow]

O

Thanks

[obsidian harness]

so the conclusion using alternate angles in parallel lines would be angle FDE = angle FED

no worries

yeah it did take me some time but I've seen stuff like this before

it really seems like your teacher did it this way too

oh no they were showing the sides DF = FE instead

[obsidian harness]

yeah, hope this helped give you a new perspective

the beautiful thing about geometry is that it can be really creative

you've barely scratched the surface of Euclidean geometry

[acoustic snow]

💀

[obsidian harness]

in schools they teach a lot of coordinate geometry, distance formula, tangents and normals, whatever

that can be boring when it's just drill and kill

[acoustic snow]

No bro the proofs on the last tests were so simple

And now he’s pulling this out

[obsidian harness]

I mean not many people will be doing maths at a pace and intensity similar to yours

especially in North America man

so yeah don't feel intimidated

your teacher has high expectations yes, but that's cause they want you to do well

it's more damaging, especially for minority individuals, when teachers give them low expectations

[acoustic snow]

😔

[obsidian harness]

you'll see this a lot throughout the education system: at college don't be surprised if the first week or two is easy, cause they need to review previous material (or otherwise students won't even understand anything later on)

and then the material just flies by

[acoustic snow]

I’m reallly good at solving

Just not proofs

[obsidian harness]

yeah it's a different area of maths

[acoustic snow]

I’m gonna do sm practice

[obsidian harness]

oh man like when I did topology I got absolutely dragged by the course

don't be disheartened there's a first time for everything

[acoustic snow]

Wait I got an ap world exam next period

[obsidian harness]

good luck!

[acoustic snow]

Thanks

[upper karma]

can someone help me with my njgpa assessment? it’s for algebra geometry & trig

i circled the ones i didn’t know in red and the ones i particularly knew in blue

[timber storm]

does anyone know how to prove that if the lines are perpendicular, then they have opposite reciprocal slope?

[upper karma]

https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/proof-that-perpendicular-lines-have-negative-reciprocal-slope#:~:text=To prove that perpendicular lines,slopes of the two lines.

this will help you more than explaining it could

[timber storm]

I tried watching that vid lol I couldn’t make sense of it

[gleaming dawn]

It’s number 14. I got the first restriction of x<-8 but I’m not sure how to the other restriction

[barren mirage]

i dont get it

[craggy fern]

is this correct?

[slate crag]

Yes

[dusk venture]

Why

X is hipotenuse

Pitágoras

Nooo

I think I made a mistake, the result is correct

The result is the same

[orchid ridge]

(im not the best explainer sorry in advance)

Remember that side lengths are always positive, meaning that the 2 given lengths are greater than 0 (4x + 48 > 0 and 8-x > 0)

With this information you can simplify the inequalities. You end up with 8 > x and x > -12

hope that helps!

[sterile snow]

Hi guys I'm seeking for solution and human being language explanation of this problem, kinda stacked at 0 point

We have a rectangle with dimensions of m x n meters, on the surface of which there is a satellite at the initial position with coordinates (x, y) (where the initial position is not on any of the sides of the rectangle). It can move around the inside of the rectangle and bounce off its walls (see picture). Assume that the satellite has negligible dimensions and consider the angle a V in the range 0 < a < 360°

1. We have specified the maximum distance D that the satellite can cover. As a function of D, determine how many different pairs (d,a) exist, where d < D denotes the distance traveled by the satellite at the angle at which it begins to move, such that the satellite stops at exactly one of the corners of the rectangle?
2. We have specified the maximum number of reflections of the satellite N. Let us calculate that the reflection by the corner of the rectangle is counted as two reflections. How many different pairs (n,a) exist, where n < N denotes the number of reflections of the satellite on the edge of the rectangle and and the angle at which it starts to move, such that the satellite stops exactly at the corner of the rectangle after exactly n reflections?

As can be seen in the image below. if we have a 3 x 3 kilometer square, starting position as in the picture and allowing at most one bounce, there are 12 different solutions. The answer in this case is V, so 12.
This task is purely theoretical, in addition to the correctness of the solution, pay attention to the procedure and justification, why your procedure is correct - why the model can be described in a certain way, why some property or algebraic modification applies, etc. Without a proper explanation of the important non-trivial steps, you will not be awarded full points.

And here some more things that I find and origanal task, in discord screenshots is some explanation of this problem but it make no sense to me

[upper karma]

damn south ur on this servver!

fyre

@south nymph taks ur here also

[trail tendon]

why...wouldn't they be?

🫠

[upper karma]

good qustion

[dusk venture]

What do you want to do with that?

Solve it?

[tardy cove]

is this right

idk how to do it

[gentle haven]

If you draw a line from the end of the 10m line all the way down, you split it into a rectangle and a right triangle

Use trig to find the portion of x on the triangle and rectangle properties for the portion on the rectangle

[tardy cove]

how would i find the angle tho

[gentle haven]

You have it

75°

[tardy cove]

ohhhhhh

ty

[gentle haven]

Np

[tardy cove]

i think i did it wrong bc i got 8.3 i did

tan(75)=21/x-10
*x-10 *x-10
(x-10)*tan75=21
/tan75 /tan75
x-10=21/tan(75)
+10 +10
x=31/tan(75)
=8.3064

[tardy cove]

also is this right

[dusk venture]

Is correct?

[coral latch]

yes

[upper karma]

Find the ratio of the areas of ABC and EBD, then use the famous: "The ratio of the areas of similar triangles is proportional to the ratios of the squares of corresponding sides."

I hope you see the similar triangles.

[obsidian harness]

Lmao why wouldn't I be ye

[upper karma]

yeah idk what drug i was on☠️

i remembered ur a math major

LOL

btw are u done with ur course? and what meth degree iz it south

[obsidian harness]

Not yet

It's a general maths degree

Stats applied and pure

[upper karma]

oh niceee

what are u going to be career wise?

(let me stop asking so many questions)

[flint marlin]

Yes

Ofc

[zealous pike]

Is A a right angle?

[upper karma]

Yes indeed.

[zealous pike]

So you already have two similar triangles

[reef moth]

how to do this question

[upper karma]

Yep, the lad probably got it.

[obsidian harness]

find the mean of -6 and -2

which has to equal a/2

[reef moth]

how to do this question

[obsidian harness]

hint

then use similar triangles

[reef moth]

this is the wrong figure

[obsidian harness]

no it's not

I mean the question wording is horrendous

I think I know what they are referring to though

[reef moth]

this is the figure

[obsidian harness]

oh

interesting

[reef moth]

ik

[obsidian harness]

you can just reflect triangle ABD across AB then

and it will be the same

that's the trick

[reef moth]

btw we have to find the height and use the basic tan formula ig

[obsidian harness]

nah the solution is elegant, you only need Euclidean geometry

I mean do it with tan if you want

[fleet summit]

I have a question where I have that the cos of an angle(the angle is called F) is 6/11, and I need to find what SinF is. Could anyone help me with that?

And the answer has to be in surd form which I’m pretty sure means it has to have a root in it

[obsidian harness]

draw a right triangle with adj = 6 and hyp = 11

use Pythagoras to find the opposite side

then you have sin = opp/hyp

[fleet summit]

Thanks, let me try that out real quick

[graceful forge]

Or use trig identity

[lavish halo]

f(x)=cos(3pi.x) what is the period of fx

[shy yoke]

.

[obsidian harness]

because cos(x) has a period of 2pi, by function transformations, f(x) has a period of (2 pi)/(3 pi) = 2/3

[stark turtle]

can someone please help

[obsidian harness]

,rccw

[obsidian harness]

try finding the diagonal length on the base first

the angle between that diagonal and the 2 kN is also 30 degrees

[stark turtle]

I don’t understand a thing trust me

[stark turtle]

oh yes

no ig its 60

[obsidian harness]

yeah and then use the 60 degree angle to find Fx

[stark turtle]

i found Fz but couldn’t find Fx and Fy

[obsidian harness]

and the other 30 degree angle you drew to find Fy

[stark turtle]

how

[stark turtle]

yup i noticed but idk what kinda calculs to use to find them I have the correction of it and it doesn’t make sense

wait lemme send it

[obsidian harness]

if you do it then $F_x = 2 \cos 30 \cos 60$ and $F_y = 2 \cos 30 \sin 60$

or $F_y = 2 \cos 30 \cos 30$, same thing

[somber coyote]

south's secret twin brother

[obsidian harness]

because x = 2 cos 30 first

[stark turtle]

oh

okay

thank you

[obsidian harness]

no worries!

hopefully this example has made you realised why there are two trig functions in spherical coordinates

[lavish halo]

ohh gotcha

makes sense ty

[upper karma]

Guys

I got ans for this

Who was want this

@everyone

<@&286206848099549185>

[tender jetty]

what?

[upper karma]

What?

[upper karma]

Bro do u need ans for this?

[tender jetty]

who are you talking to

[upper karma]

xD

[civic forum]

Lol

[boreal burrow]

What is the ans

[grim plume]

wtf is this

I’m supposed to have an answer but I’m getting ssa which isn’t right

[silent plank]

how are you getting ssa

[grim plume]

cause

ssa

ba is an s

ac an s

and c is the a

[silent plank]

wdym by c is the a

[grim plume]

they both have c

isn’t it congruent because of that

[silent plank]

wdym by the both have c

[grim plume]

abc and cde

they both contain the point c

[silent plank]

can you clearly indicate which things you're saying are congruent in the pic

[grim plume]

Abc = cde

that’s what I have to prove

C is a congruent point because they both use the single point

AB=CD because that’s given

AC=CE because C is the midpoint

I is dunno what proves BC and DE

[silent plank]

having a common point doesn't say anything about congruence

[grim plume]

what?

yeah no

not gonna bother

[silent plank]

in congruence justifications,
S refers to congruent sides
A refers to congruent angles
H: hypotenuse, L: leg (these two aren't relevant to the question)

try identify which other angles / sides are congruent

[dreamy vessel]

This exact question got asked like 2 weeks ago 💀 It's impossible mate

[flint marlin]

Bruh

Point c doesnt even matter

Its about angle

[tawny mango]

.

[obsidian harness]

what is angle CAB?

[tawny mango]

dw i figured it out

i got another tho

[obsidian harness]

ah that's neat

[tawny mango]

very hard i have no idea how to do it

[obsidian harness]

the alternate segment theorem would really help

angle ABC = angle ACE

[tawny mango]

this is what i got so far

[obsidian harness]

then all that remains to do is to find angle CAD

[tawny mango]

Angle ACE = 83

[obsidian harness]

yep

[tawny mango]

Angle ADC = 97

opposite angles in cyclic quad = 180

[obsidian harness]

that's correct but that probably isn't useful

[tawny mango]

mhm

[obsidian harness]

try finding CAD instead

[tawny mango]

yeah thats where im stuck i have no clue

CDE = 83 btw

[obsidian harness]

hint: bowtie

[tawny mango]

yeah icl i either have not learnt that or have learnt it but in a different name

[obsidian harness]

the circle theorem is called angles in the same segment

see, it looks just like a bowtie actually

[tawny mango]

oh yes i see ive learnt that one

lemme see if i can aply it here

ACD = 37

DAC = 46

[obsidian harness]

try using that theorem on the 46 degree angle instead

yep

[tawny mango]

alr thanks so much man i can probably do it from here

[jade sierra]

I just started doing right triangles on like em circles

And this is how I know I’m cooked

[trail tendon]

so...trig?

[vagrant snow]

I mean he did say he's cooked

[trail tendon]

when i think of trig i dont think of cooked

unless its those horrendous trig problems

with ridiculous identity manipulations

[vagrant snow]

I mean like he called it "right triangles on like em circles"

[trail tendon]

sounds like normal trig 🫠

[vagrant snow]

Welp

Unit circle moment

[tawdry arrow]

i have a geometry test on monday i am so cooked

i was sick the first day of the unit and missed so much info

[trail tendon]

😭

[upper karma]

Not impossible

Bro we got all the Gevin

This is rhs triangle

Angel b is right angle

Then there is an angle with 30 and Angle with 60

Then if u remember at last there is a rull tell us that rhs triangle the ab is half the hypotenes

Then wait let me draw it

[silent plank]

if you are given all the angles (not mentioned in your original image) then yeh, it's possible

[upper karma]

Yeah

Wait bro I'm drawing

This is all my mind got but wait

We can use angle c

Wait

[fair herald]

How did you find AB = 2AC

[upper karma]

Lol cuz it's a rhs triangle

[fair herald]

Define rhs

[upper karma]

Right hypotenes side triangle

[fair herald]

So basically a right angled triangle?

[upper karma]

Yeah

So the angle c = 30

[fair herald]

Ngl i dont think that rule is a thing

[upper karma]

So we will use tan

[upper karma]

Bro in Egypt we learned that

[fair herald]

Hmm lets say x = 5

Ac = sqrt(11^2+5^2)

AC = 12.05

Which is not 5*2

Idk man

[upper karma]

I still didn't learn the sqrt

[fair herald]

Sqrt is square root

[upper karma]

Oh

Bro try

[fair herald]

What did u find x to be?

[upper karma]

Sqrt 3
11

That what i find

[fair herald]

So 11 or sqrt 3?

[upper karma]

Sqrt 3 fraction 11 in down

What did u find

[fair herald]

Its impossible bro idk

U can put x as any value and itll work

[upper karma]

If x = sqrt 3
---------
11

[upper karma]

Yeah

[fair herald]

If u put x = 50 itll still worm

Work

[upper karma]

Then x can be

[fair herald]

X can be 0 < x < infinity

[upper karma]

Then this work

I can't believe it's solved

[fair herald]

I think the answer is 0 < x < infinity 💀

If we using ur "rule"

[upper karma]

Idk bro it's not mine we really learn that in Egypt

[fair herald]

I think u misheard it or smth

[upper karma]

Wdym

[fair herald]

Like u thought it was smtg else

[upper karma]

No i just want to know what do you mean by misheard it

[fair herald]

Yeah like u thought it was a rule or smth but it was smth else

[upper karma]

U think that really

[fair herald]

Yeah because there is literally an infinite amount of answers

[upper karma]

I will ask my teacher today

[fair herald]

Unless its given that AB is X and AC is 2x

[upper karma]

I put this

[fair herald]

If it is given by the question then yes ud be correct but if not then its impossible

[upper karma]

This is the one who i was solving

In my mind nothing is impossible

[vagrant snow]

What's your solution to this?

[vagrant snow]

It's not that it's impossible it's that there are infinite possible values for AB and AC

[obsidian harness]

yeah that clearly has infinitely many solutions

[flint marlin]

Sucks to be you , respecting geometry is a crime

[upper karma]

Wait let me send it

That is all what i got

[upper karma]

What do u want

[flint marlin]

Why

[upper karma]

As a right hypotenes side triangle

[flint marlin]

Where is it given that AB = 1/2 AC

[upper karma]

Not given

[flint marlin]

How do you assume then?

[upper karma]

Rhs triangle

[flint marlin]

Does that mean a triangle with sides 3 , 4 and 5 is not right angle ?

[flint marlin]

Whats rhs triangle?

Rhs is used to prove two right angle triangles are congruent

[upper karma]

This is the triangle that have
Right angle
Hypotenes
And normal side

[flint marlin]

There's not called rhs triangle

[flint marlin]

Its a right angle triangle

[upper karma]

This is what we learned in Egypt man

[flint marlin]

So you mean egypt ppl are dumb to teach wrong stuff?

[upper karma]

Please don't talk in bad way

[flint marlin]

I am sorry hut

But *

Nvm

Here

This is what RHS mean

[upper karma]

U used it to try to get the ab

[flint marlin]

You cant

Data is insufficient

[upper karma]

I know i feel like i did a problem in it but of course it's able to solve

[flint marlin]

Nah bro you just cant

Never

Ask anyone

[upper karma]

U think it cant be solved

[flint marlin]

If you dont trust me

[flint marlin]

I dont think ITS true

Ab and ac has infinite possible values

[upper karma]

Yeah that's a problem

[flint marlin]

Thats a problem?

[upper karma]

Yeah

Bro we at least need one more side

[flint marlin]

EXACTLY

[upper karma]

Yeah but

[flint marlin]

THATS WHAT I MEAN BROTHER

[flint marlin]

But?

[flint marlin]

Hence data insufficient

[upper karma]

Why i feel that it can be solve

[upper karma]

Yeah

[flint marlin]

Nope , it just can't be

[lyric snow]

I need a bit of help with Geometric Constructions

[upper karma]

are any of you familiar with voronoi diagrams?

[obsidian harness]

just post your question here

enjoy solving this if anyone is up for a challenge

[wary talon]

75

[obsidian harness]

did you do this question before, lol

or did you spy on the help channel

75 is correct

or did you Google it

[wary talon]

Nope, it is just pretty easy

[obsidian harness]

wow

[obsidian harness]

here's what I did btw

[wary talon]

I did it this way

[obsidian harness]

ohhhhhhhh

yeah I wanted to draw that line but I didn't see how at first

yeah that makes so much sense now

[inland linden]

bro this is 8th grade material

[obsidian harness]

it's in Cambridge's entrance test for engineering so

congrats if you know how to do it

[rustic rampart]

it is

[trail tendon]

a REAL engineer would measure it 😁

[vagrant snow]

Pythagorean theorem just went out the window in Egypt ig

[graceful talon]

Let s be the side of a cube. What is the body diagonal the cube?

⚠️ SPOILER ⚠️ the answer is ||s√3||

but how would you find it?

[trail tendon]

wdym the "body diagonal the cube"

[graceful talon]

the diagonal from one corner to the opposite corner

[trail tendon]

so...the line?

[graceful talon]

idk what's the proper term for it

[graceful talon]

yea that line segment

[trail tendon]

thats not the answer is it

[graceful talon]

maybe i can find a picture

[trail tendon]

i'm not sure i understand the question

the "body" is a line segment?

[graceful talon]

like this

[trail tendon]

yeah

so its a line...

[graceful talon]

i said body to distinguish it from the surface diagonals

[trail tendon]

what is the diagonal of the cube? the diagonal is a line

do you mean length or smthn?

[graceful talon]

yes the length

[trail tendon]

oh...

[graceful talon]

let s be the length of each side

[trail tendon]

can't you just use the distance formula lol ._.

sqrt(s^2 + s^2 + s^2) = sqrt(3s^2) = sqrt(3)s

[graceful talon]

ohhhh

wow that's different

[trail tendon]

or, like the "pythagorean theorem" in 3d 💀

[graceful talon]

i see. interesting

yea. I just knew how the formula was derived

from what I read, you find the surface diagonal of the bottom surface

then use Pythagorean theorem to find the diagonal. your sides would be the bottom surface diagonal and the other side

,,r=\sqrt{2s^2}=s\sqrt{2}\
d=\sqrt{r^2+s^2}=\sqrt{(s\sqrt{2})^2+s^2}=s\sqrt{3}

[trail tendon]

yeah that works as well

[somber coyote]

0_א

[upbeat jungle]

Wrote down the unit circle (I have a quiz on it tomorrow so Im trying to remember it)

[weak plaza]

can someone help me with this

[weak plaza]

tell me if you find a short cut to remembering all that

[upbeat jungle]

Quad 1, denominators 6,4, and 3

Quad 2, (x/cos) is negative and numerators are 1 less than denominator

Quad 3, (X and Y/ Cos and sine are both negative) numerator is 1 more than denominator

Quad 4, (Y/sine is negative) numerator is quad 2’s numerators + the corresponding denominator

30,150,210, and 330- denominator of 6
45,135,225, and 315 - denominator of 4
60,120,240, and 300 - denominator of 3

This is how I’m trying to remember it

[upbeat jungle]

Also
0/360- (1,0)
90- (0,1)
180- (-1,0)
270- (0,-1)

[trail tendon]

you remember the difference formula for sine?

[weak plaza]

yeah i figured it out thanks

[weak plaza]

damn even this is annoying to remember all together

[upbeat jungle]

This was easy to remember after I recognized the pattern

[lyric halo]

What the hell is a polar

and a pole

[trail tendon]

polar is related to things near the north pole, such as a polar bear

[trail tendon]

a pole is something you ram your head against when you're doing math

💀

nah polar is an axis, where you determine points by the radius and angle rather than the x coordinate and y coordinate

[lyric halo]

can we take an example

[trail tendon]

sure

[lyric halo]

do you mean polar coordinates?

[trail tendon]

yeah

is that not what ur talking about? 💀

[lyric halo]

oh im not talking about them

[trail tendon]

what ARE you talking about then?

[lyric halo]

I'm talking about the pole and polar

[trail tendon]

hm idk then 😂

[trail tendon]

do you have an example of what ur talkin about?

[lyric halo]

@trail tendon

[trail tendon]

hm yea idk

[graceful talon]

,w polar of a point

[somber coyote]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by lkjsfkjsiu

[graceful talon]

idk

[modest hull]

,w polar of a point circle

[somber coyote]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by deltalamma

[modest hull]

,w polar of a point circle

[somber coyote]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by deltalamma

[modest hull]

hm

,w polar of a point

[somber coyote]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by deltalamma

[obsidian harness]

it's called power of a point

@graceful talon

[graceful talon]

ohhh

[modest hull]

ah, fair

[graceful talon]

but what is it

,w power of a point

[somber coyote]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by lkjsfkjsiu

[graceful talon]

idk

[obsidian harness]

Google

[graceful talon]

someday i will need the definition

[maiden brook]

there are polars of points also though

[upbeat jungle]

Rewrote my unit circle notes cause i have a quiz next class

[lyric halo]

A) Range of f(x)

B) Period of f(x)

C) Check if the following are true or not:
a) f(x) = 4 has real roots
b) f(x) = 1 has real roots

D) Range of f inverse (x)

I got the tangent

wait is this correct?

[lyric halo]

solved, nvm

[cyan steppe]

I think the 2nd one is correct, Idk if you have solved it or not.

[marble cliff]

is there someone who can help

with projective geometry

[rapid valley]

Yo

Anyone here know how to graph the points in between the x coordinate and the period in a trig function?

Or find the points

Better way to say it

[upbeat jungle]

Parent points are 0, pi/2, pi, 3pi/2, and 2pi or are you talking about something else?

[zealous pike]

If Cos is x and Sin is y on the unit circle, what are cosecant and secant?

[upbeat jungle]

Think their inverses are still the same on the x y axis

So cosecant at 30 degrees would be 2/root3

[cunning lion]

you can construct them from the unit circle like so

but most of the time it's easier to just use 1/cos and 1/sin

[graceful talon]

i think you can also do like which side of the triangle you choose to have length 1

if hypotenuse is 1, the sides are sin and cos

if x-side is 1, the hypotenuse is sec and y-side tan

and if y-side is 1, hypotenuse is csc and x-side is cot

[graceful talon]

$$\sin^2\theta+\cos^2\theta=1\\$$
$$\tan^2\theta+1=\sec^2\theta\text{ (divided by} \cos^2\theta\text{)}$$
$$1+\cot^2\theta=\csc^2\theta\text{ (divided by}\sin^2\theta\text{)}$$

[somber coyote]

0_א

[rigid tangle]

Can anyone help me

🧍🏽

I don’t get my math hw

[waxen rapids]

I have a skill issue

[trail tendon]

does it ask for the diameter?

[waxen rapids]

yup

I got the answer right

but apparently I didn't

like it says the answer is 18 but I didn't enter in the right 18 apparently

[trail tendon]

bro you're so bad the answer is obviously not 18, clearly the actual answer is 18 🤦‍♂️

[waxen rapids]

I know I know

[trail tendon]

[waxen rapids]

I'll fix it next time

[trail tendon]

you'd better 😤

[waxen rapids]

😭

[trail tendon]

🤣 😭 a.i. grading go crazy

chat GPT but in grading homework

[waxen rapids]

naw fr

[trail tendon]

still somehow screws it up

[waxen rapids]

this SAT practice

apparently it doesn't know what numbers are tho

[trail tendon]

my best guess is you probably put a space in front or something but 🤣

[waxen rapids]

maybe it thought it was 78 because the font

[waxen rapids]

I checked that

no space

just plain tomfoolery

[trail tendon]

maybe it wants a space?

[waxen rapids]

went from 90% to 80% off of that lol

[trail tendon]

making things up at this point

[graceful talon]

where is the law of sines

,w law of sines

[somber coyote]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by lkjsfkjsiu

[graceful talon]

it should be pinned too

[main fiber]

A circle has an area of 33 pi cm squared and a central angle of 11pi over 6 rad find radius

my teacher says its 6cm but when i solve it i dont get anywhere near that

using the formula a=1/2rsquared theta

nvm i got it

[plucky knoll]

hello, I'm working on a vector problem, and i am wondering how the answer for the total x and y values were found, because the addition looks wrong. here is the marking schedule with the calculation that im confused about

[plucky knoll]

the thing im confused about is how (992.82) + (-239.41) = x value of 1232.23, and how (-119.62) + (-657.78) = y value of -538.16

[shy hearth]

Hi! Does anyone know an efficient method to solve this?

I'm trying using tan half angle t substitution, but I'm hoping there's a solution that doesn't require as much algebra

[regal hawk]

I think you should simplify the RAEs first

[graceful talon]

what is RAE

[regal hawk]

the ratio

[graceful talon]

I'm thinking of the acronym

what could it be

Ratio And Exponents?

[regal hawk]

rational algebraic expressions

its used in our country

its in the form of p(x)/f(x)

[graceful talon]

I see. Thanks

[timber turret]

hi there, am I just supposed to ignore the 3.25 cause it's not lining up with the graph? I checked if it's a rounding error and it wasn't, please ping if u could help

[obsidian harness]

where is there a 3.25?

[faint pasture]

Can someone link to a decent proof for the area of rectangle/triangle

I have probably been using those formulas everyday without knowing a proof

Nd yea dont mention the math stack exchange page almost all the solutions there assumed integer side length

[simple lotus]

Guys

BD and AE are the bisectors of triangle ABC. A line parallel to AE is drawn through point D and intersects side BC at point F. Find BC if FC = 5cm

Help me

[hoary prism]

Did you draw out a picture of it?

[simple lotus]

Yh @hoary prism

I did

Soo

@hoary prism help

Please

[fathom ocean]

be patient

[simple lotus]

Sorry

Its like

12 am

For me

I havent sleep for days

I beg you

Help me someone

Who Should i ping

To get help

[fathom ocean]

like i said, be patient. if someone is willing to help, they will; spamming is not going to take it anywhere

[simple lotus]

Sssorry

Uhh

Are u good enough to help me?

[fathom ocean]

no

what have you tried doing, though?

[simple lotus]

I am stupid I didnt do anything

@hoary prism Iiiii beg u and sorry for sppam

Hhelp me

[waxen sun]

are you aware of the basic proportionality theorem and other similar theorems related to triangles

those will help in this question

similarity too

[hoary prism]

yeah

[hoary prism]

bro calm tf down first of all

second of all notice that CFD and CEA are similar

find the scaling factor and then work out the rest

[simple lotus]

What is scaling factor

I just eant the solution please help me then i will understand everything

And I am 8th grade

[hoary prism]

in a similar triangle if you know that one of the sides is scaled by some amount then you know that the rest of the sides are scaled by the same amount

[hoary prism]

so you know how AC and DC are related in these two triangles, the length of DC is half of the length of AC because D is the midpoint

what can you say then about the length of EC based on the length of FC?

[simple lotus]

We cant know it fc is just a part of it not a half

[hoary prism]

see here

we can know the relationship between FC and EC because we know the relationship between two other corresponding sides

[simple lotus]

OH

ITS 5 AGAIN?

[hoary prism]

FC is 5, what does that make EC

[simple lotus]

10?

[hoary prism]

yeah

so now you know EC is 10, what does that make BC

[simple lotus]

20?

[hoary prism]

yeah

that's it

[simple lotus]

Ah thx

[hoary prism]

np, but just a word of advice if you're really persistent like this people are gonna be less inclined to help out

[simple lotus]

But i didnt learned abt it in school i could be suspicious btw AE is paralel to DF maybe we can make another solution?

[hoary prism]

what other kind of solution?

[simple lotus]

Like we are learning tables and things that have 4 sides and the sides are paralel

2 are pararel and 2 as well

Table is the thing which 2 sides are paralel and 2 are not

[hoary prism]

like a trapezoid?

[simple lotus]

Idk maybe

[white dune]

What is the difference between a triangle and a square asking for a friend?

[hoary prism]

in this case it would just be overcomplicating the problem

[hoary prism]

square is a polygon with 4 sides all of equal length and all sides intersecting at right angles, triangle has 3 sides not necessarily of equal length

[simple lotus]

Here they are

[white dune]

Yeah but how is that different from a triangle

[hoary prism]

edited

[hoary prism]

yeah on the bottom is a trapezoid, on the top is a parallelogram

[white dune]

Thanks man you helped my friend out a lot

[hoary prism]

i dont see how its related here

[simple lotus]

Idk

Maybe we can use some tricks of the tales theorem?

[hoary prism]

idk how to interpret your question tbh, given any triangle you can glue another copy of the triangle onto one of its matching edges and form a quadrilateral, here its not necessary to do that

cause youre just computing something about a similar triangle inside the triangle

[simple lotus]

Ah ok

I have one more question

Prove that the midpoints of a pair of opposite sides and diagonals of a quadrilateral without parallel sides are vertices of a parallelogram

[hoary prism]

i mean the best way i can think of to do this is by agreeing that we have some notion of a unit length, and that a 1x1 square has an area of 1, then you can build any rectangle out of 1x1 squares and derive the length*width formula from there, and for triangles do a similar thing where you notice that any triangle can be formed out of two right triangles glued together and derive the formula for an area of a right triangle by noticing that its always half of the rectangle with width and height equal to the two legs of the right triangle that meet at the right angle

[hoary prism]

attempt it and see where you get stuck

[marble cliff]

is someone here good in projective geometry

How is the second picture a side viwe of the first picutre

[cyan steppe]

Bro just observe the triangle ACE in this, in that triangle DF is parallel to AE, then if you know the Basic Proportionality theorem, you can write

CF/FE = CD/DA
→ CF/FE = 1 (since CD = DA)
→ CF = FE = 5 cm

And since BC = BE + EC
→ BC = EC + EC (since BE = EC)
→ BC = 2EC = 2(EF + FC)
→ BC = 2(5+5) = 20 cm.

[wind swift]

can someone help with this question? Me and one other dude are stumped.

"In convex pentagon ABCDE, segment AB is parallel to segment DE. The measure of angle B is 139 degrees, and the measure of angle D is 174 degrees. What is the measure, in degrees, of angle C?"

[worn stag]

I think for the square you need to make the condition stricter by specifying that the angles are right angles

[faint pasture]

That only works for integer side length

[hoary prism]

yeah youre right

[hoary prism]

what i said has nothing to do with integers tho

your unit length can be whatever

the same argument works if you have a 2.5x2.5 square if you want

or a pi by pi square

it would just scale

[faint pasture]

Howd you do this?

[hoary prism]

say i wanted to build a 10x5 rectangle or something and i started with a pi by pi square, then i can just scale it down by dividing each side by pi and get to a 1x1 square with an area of 1, then i have 5 rows and 10 columns of squares so 50 total, then summing up the areas you get 50

nothing's dependent on integers here

i could also multiply each side of the 10 by 5 rectangle to get 10pi by 5pi

and then not scale the square

[faint pasture]

The proof to why we can scale down stuff?

[hoary prism]

i mean its just how real numbers work, if i stick this on a grid and say that my square is bounded by 4 coordinates, then i can send that to a square that's scaled down and describe the coordinates of those

so in this case its like

lets say (0,0), (0,pi),(pi,0),(pi,pi) are the corners of the square we start with

[faint pasture]

💀 is that like an axiom?

[hoary prism]

each side is of pi length, then scaling it down i get to (0,0),(0,1),(1,0)(1,1)

[hoary prism]

well its the notion of distance that youre working with implicitly

[faint pasture]

But we dont exactly know if scaling down doesnt change the area i mean yes we know but we havent proved it

[hoary prism]

the distance between any two points (a,b) and (c,d) is just sqrt((a-c)^2 + (b-d)^2) and analogously for higher dimensions

[faint pasture]

Ye

[hoary prism]

i mean you kinda have to take on faith that we can define a unit length and a unit area for this, otherwise i think to go deeper we'd need to talk about measure theory

[faint pasture]

So like if you consider this we havent proved that area(old square)= pi^2 area(new square)

[hoary prism]

how so?

if you want you can like

draw them, and then split the remainder of the bigger square into smaller rectangles

then add them up

[faint pasture]

💀 thats just sad one of the most basic formula and no proof in sight

[hoary prism]

idk

[faint pasture]

Hmmm

[hoary prism]

i mean this is just a euclidean space axiom

[faint pasture]

Thanks anyways