Needing help on similar triangles for geometry pls and thanks

[soft thunder]

are you familiar with tangent?

[worthy summit]

no i’m not

[soft thunder]

have you heard of sine and cosine before?

[worthy summit]

no i havnet im in like geometry in my highschool so i’m not really familiar with that so

[soft thunder]

okay so basically there are three functions which can be applied to right triangles

sine, cosine and tangent

[worthy summit]

Okay and what does that mean?

[soft thunder]

each one of them describe a ratio between certain sides of the triangle in regards to an angle

[worthy summit]

oh okay i understand now, the part i get confused with it when to add and subtract the congruent sides of the two triangles that overlap

and how to set the equation up properly

[soft thunder]

these are the side of a right triangle when viewed from any angle

[worthy summit]

Okay got it

this is the problem right now, and i don’t know where to add or where to subtract to start the equation

[soft thunder]

that's why you should let me finish

[worthy summit]

sorry

[soft thunder]

here, this is what the ratios look like for each function

now when we apply this to your problem can you name which sides we have currently measured?

[worthy summit]

hypotenuse?

[soft thunder]

the hypotenuse is the longest side, opposite of the right angle in the triangle

[worthy summit]

ohhh, so would it be the adjacent side that is already measured?

[soft thunder]

not only that

[worthy summit]

opposite as well?

[soft thunder]

now give me the measures for both sides

[worthy summit]

opposite= 120.24m adjacent=130m

[soft thunder]

.25 but yes

[worthy summit]

yes sorry i just recognized my error

[soft thunder]

now let's look back at this

any ratio we could use?

or function, rather

[worthy summit]

120.25
————
130

?

sorry i tried my best to make a fraction

[soft thunder]

not a problem

don't forget the units

[worthy summit]

okay sorry

[soft thunder]

so it would be 120.25m/130m

[worthy summit]

okay got it

[soft thunder]

now if you punch that into your calculator and hit the tangent function, what do you get?

[worthy summit]

is there a fraction button on an iphone calculator?

[soft thunder]

uhm

just type 120.25 divided by 130

[worthy summit]

okk

[soft thunder]

a fraction is just a division in the end

[worthy summit]

0.925

is what i got

[soft thunder]

yep

now we actually don't use tangent but cotangent

which is the inverse

[worthy summit]

Okayy

[soft thunder]

right now we have 0.925 which is the ratio which we can convert back to an angle

[worthy summit]

how do we do that?

[soft thunder]

by using the cotangent function

do you have that on your calculator?

[worthy summit]

i think there’s a button that says “tan”

is that it?

[soft thunder]

yes

but that is tangent

you will need the inverse

so cot

[worthy summit]

i may not have that i have cos and tanh

[soft thunder]

do you have a secondary function on your calculator?

[worthy summit]

yes

[soft thunder]

try to press that

maybe it gives you cot

[worthy summit]

it doesnt show it says same things with like a -1 at the top of each function

[soft thunder]

yes

that is the inverse

[worthy summit]

oooh ok ok, so which would i press? cos-1?

[soft thunder]

tan^-1

[worthy summit]

okay so what numbers do i put into it same ones?

[soft thunder]

remember, we were using the tangent function since we had a ratio of opposite to adjacent

[worthy summit]

0.925?

[soft thunder]

yes, 0.925

[worthy summit]

42.76

is what i got

[soft thunder]

that doesn't sound right

are you sure you had 0.925 and hit the secondary function before pressing tan?

[worthy summit]

ill try again

[red prairie]

I need some help too

[soft thunder]

in a second

[worthy summit]

yes i got 42.76882539 and so on

but i have to round the nearest hundredth of a meter

[soft thunder]

well it gives me 61.936 approximately

[worthy summit]

tan^-1 right?

[soft thunder]

yes

[worthy summit]

yeah i got the same number again

[soft thunder]

hm, try resetting your calculator

type in 0.925 and then try again

[worthy summit]

yeah i got the same thing

[soft thunder]

can you show me a screenshot if that's possible?

or are you using an analog device

[soft thunder]

what happens when you hit tan?

with the 0.925

[worthy summit]

0.016

[soft thunder]

now hit the 1/x

[worthy summit]

0.016 converts to 62.5

but with 0.925

goes to the 42 number and then to 61.93

[soft thunder]

aha

well I think your calculator is a bit faulty

you should maybe get an analog one

[worthy summit]

yes i agree

so i have to go to tan the 1/x

[soft thunder]

yes for now that will suffice

I recommend using an online calculator tho

anyways

[red prairie]

Helpppppp

[soft thunder]

I'd appreciate it if you opened a second channel

[red prairie]

I am new

How to open?

[soft thunder]

#❓how-to-get-help

or #1021175428326633542

so now that we have the 61.936

can you tell me what that number means?

[worthy summit]

opposite?

[soft thunder]

look back here

[worthy summit]

hypotenuse / adjeent?

adjacent*

[soft thunder]

repeat to me what we just did please

[worthy summit]

we divided 120.25m by 130m

[soft thunder]

because of what?

[worthy summit]

which was opposite over hypotenuse

[soft thunder]

that is incorrect

[worthy summit]

oh

we used the tan function so opposite over adjacent

[soft thunder]

exactly

now what are we aiming for with that?

[worthy summit]

x

[soft thunder]

if you remember I mentioned that it's a ratio regarding an angle

do you see the θ?

[worthy summit]

no i dont

oh wait yes sorry

[soft thunder]

you'll see it

[worthy summit]

i thought u meant the problem

[soft thunder]

ah no

for now I want to clarify why we did this

you can see it says tan θ

correct would be tan (θ) btw because it is the tangent of theta

can you tell me what θ is?

[worthy summit]

61.93

[soft thunder]

yes

but also what is θ

[worthy summit]

the answer coming out of dividing opposite and ajdacent

[soft thunder]

look at the picture again

look to the right

[worthy summit]

the right angle

[soft thunder]

where is the symbol

θ

[worthy summit]

inside the triangle to show the angle

[soft thunder]

exactly

it represents an angle

this is very important

so the tangent of theta (written as tan (θ)) is equal to the ratio of opposite to adjacent

which is why we inversed the ratio with the cotangent to "restore" the angle we are searching for

do you understand this?

[worthy summit]

yes i do

so the answer would be 61/93

61.93*

[soft thunder]

well if we were searching for the angle then yes

[worthy summit]

Okay let me try putting it in

[soft thunder]

but we will have to do one more step

[worthy summit]

Oh okay

[soft thunder]

we are not searching for the angle in your problem

https://cdn.discordapp.com/attachments/1063234087290146847/1063236245322477628/D988FB81-86A5-47EC-95F6-2B647778BE51.jpg

we are searching for the length of VW

but what can we do now that we know the angle at point U?

[worthy summit]

add that with 70m?

[soft thunder]

think in mathematical terms

what are we searching for?

[ancient panther]

You don't need to use tangent to solve this problem. This is a question abt similarities and ratios

[worthy summit]

the missing variable? or the length of VW

[soft thunder]

...

we are onto something here I don't understand why you would have the urge to barge in

[ancient panther]

Because obviously he hasn't learned trignometry yet

[soft thunder]

so what

you take away his freedom by deciding for him whether or not he should be learning this stuff now

I think oz7 would've let me known if he was against the way I am trying to get this through

[worthy summit]

yeah i dont mind

[soft thunder]

precisely my point

[ancient panther]

So triangle VWU and triangle XYU are similar triangles,
VW:XY=VU:XU

I'm just trying to say there's a simpler solution

Sorry to interrupt, I'll leave now

[soft thunder]

you should've said it at the end

so now that you know there's an easier method, which one do you prefer

[worthy summit]

continue with yours

[soft thunder]

alright

[worthy summit]

id rather learn this early so i understand it next year

[soft thunder]

love it

[worthy summit]

yes

[soft thunder]

okay let's refresh

we have established an angle of 61.936 at point U

by using the cotangent

we also know that we are searching for the length of VW

[worthy summit]

indeed

[soft thunder]

using this picture once again

can you tell me what VW could also be viewed as?

[worthy summit]

opposite

[soft thunder]

you're getting the hang of this

so what can we use to calculate it?

look closely at your problem and at the picture I provided and you should be able to figure it out

[worthy summit]

opposite and hypotenuse

[soft thunder]

remember, hypotenuse is opposite of the right angle and the longest side

[worthy summit]

ohh oky so opposite and adjacent again?

[soft thunder]

you can't use the opposite to calculate the opposite

[worthy summit]

good point

so then adjacent and hypotenuse?

[soft thunder]

look at the left side

remember what we calculated

[worthy summit]

im not sure

[soft thunder]

what function did we use?

[worthy summit]

opposite and adjacent

[soft thunder]

these are just names, not a function

[worthy summit]

ohhhh

tan and 1/x

[soft thunder]

yes

let's just say cotangent

[worthy summit]

thats the one we use for VW?

[soft thunder]

no that's what we used to reverse the ratio into an angle

remember?

[worthy summit]

yes i remember

[soft thunder]

okay good

so spin up these brain cells of yours

what measures do we have at hand which could be useful to calculate the opposite?

[worthy summit]

XY

[soft thunder]

you can do one better

[worthy summit]

XU?

[soft thunder]

close

[worthy summit]

YU?

[soft thunder]

precisely

what is YU?

[worthy summit]

61.93

[soft thunder]

no that was the angle

[worthy summit]

its the hypotenuse?

[soft thunder]

is it opposite of the right angle?

[worthy summit]

yes? i think

[soft thunder]

if you look at the picture the square indicating the right triangle is right next to point Y

so it's adjacent, not opposite of the right angle

[worthy summit]

ohhhhhhh

[soft thunder]

what is YU then?

[worthy summit]

adjacent

[soft thunder]

only one option left

you got it

and what is its measure?

[worthy summit]

120.25m

[soft thunder]

careful

[worthy summit]

im not sure of the measure

[soft thunder]

nvm I fucked up

I didn't see the points

I meant VU the whole time

YU was the hypotenuse

[worthy summit]

ohhhhhhhh

[soft thunder]

LMAO

excuse me

[worthy summit]

all together VU woulld be 200m?

[soft thunder]

yesyes

omg that must have caused a lot of confusion

I'm a terrible teacher

[worthy summit]

lol its okay dw

no ur not ive learned a lot so far

[soft thunder]

thanks but that's really shouldn't have happened

panik

[worthy summit]

haha its ok

[soft thunder]

yeah let's continue

let's use my trusty picture again

can you tell me what to do?

[worthy summit]

we have to do adjacent over hypotenuse

[soft thunder]

remind yourself of what measures we calculated so far

write them down

[worthy summit]

VU

and point U

[soft thunder]

not point U

[worthy summit]

Yu?

[soft thunder]

no we calculated the angle at point U

[worthy summit]

ohh ur right sorry

[soft thunder]

and what was VU again?

[worthy summit]

200m

[soft thunder]

and furthermore?

[worthy summit]

Vw is 200m

[soft thunder]

what

no

I was asking for what VU is else

apart from 200m

[worthy summit]

hypotenuse?

cause yu was adjacent

[soft thunder]

no I mixed it up

[worthy summit]

so VU is adjacent?

[soft thunder]

yes

[worthy summit]

ok got it

[soft thunder]

since it is adjacent to the angle, but not opposite of the right angle

the hypotenuse is also always the longest side on top of being opposite of the right triangle

[worthy summit]

so it will always be thee longest side?

[soft thunder]

the hypotenuse will always be the longest side, yes

[worthy summit]

okayy

[soft thunder]

so now we have the adjacent VU with a measure of 200m and the angle at point U with a measure of 61.936°

[worthy summit]

correct

[soft thunder]

and we are searching for the opposite

what is our only option to solve this problem then?

[worthy summit]

function sin

[soft thunder]

how

you would need the hypotenuse

[worthy summit]

so cos?

[soft thunder]

I just said we have an angle, the adjacent and we are looking for the opposite

no hypotenuse

whatsoever

[worthy summit]

so the only option left is tan

[soft thunder]

yes

the tan function seems to be working on your calculator

[worthy summit]

yes it is

[soft thunder]

so you can put the measure of the angle in there and tell me what the result is

but

if you are really smart you already know the result

[worthy summit]

0.925?

[soft thunder]

and why would that be

[worthy summit]

because 61.93 came from 0.925 and therfor just reverted back

[soft thunder]

because we used the inverse of the tangent on 0.925 to restore the angle it follows that if we use the tangent on the angle we get back our ratio of opposite to adjacent, in this example 0.925

but yes, you got it

[worthy summit]

woo okay okay

what we do from here

[soft thunder]

well now we have a fairly simple equation

0.925 = opposite/adjacent

you should be able to figure this out, if not let me know

[worthy summit]

so would the equation be 0.925/200?

[soft thunder]

careful

you want the opposite to stand alone on one side of the equation

[worthy summit]

0.925/x = 200/61.93?

[soft thunder]

0.925 = opposite / 200m

how do you get rid of the 200m on the right side?

[worthy summit]

im confused

subtracting

200

[soft thunder]

it's a fraction

you can't just subtract

[worthy summit]

dividing 200?

[soft thunder]

the opposite is being divided by 200m already

why would you want to divide it by a further 200

that would split it into even more parts

[worthy summit]

but whats the opposite im confused on that

[soft thunder]

the opposite is VW

[worthy summit]

so if VW is the opposite

and VU is adjacent

which is 200

than the adjacent is YX?

[soft thunder]

no the adjacent is VU

[worthy summit]

hypotenuse?

sorry i typed without thinking properly

[soft thunder]

look

0.925 = VW / 200m

I can't make it easier without solving it

let's take a little detour

to explain what you are meant to do

[worthy summit]

okay ya cause i still dont know how to solve

it

[soft thunder]

if I give you the number 1

and then tell you to split it into 2 parts, how would you write that?

[worthy summit]

1/2

so 0.5

[soft thunder]

was about to say

so how do you get back your 1 now?

[worthy summit]

0.5x2

equals 1

[soft thunder]

keep the fraction

[worthy summit]

1/2

[soft thunder]

now do the same thing

[worthy summit]

200 would be 100 in two parts

[soft thunder]

please stay here

don't wander off

[worthy summit]

okay i wont

[soft thunder]

1/2, how do you get back your 1?

[worthy summit]

by adding another half

[soft thunder]

no

that's not what this is about

[soft thunder]

look here

you did it before

I just wanted you to write it as a fraction

[worthy summit]

0.5/2?

[soft thunder]

what did you write

[worthy summit]

0.5x2/1

[soft thunder]

you wrote 0.5 x 2

[worthy summit]

yes

[soft thunder]

all I want is for you to use fractions

don't use 0.5

that's literally all I wanted

[worthy summit]

erm

so

would it be

5/2

[soft thunder]

what happened to your 1/2

[worthy summit]

idk how to make it to afraction

[soft thunder]

you made 1/2 into 0.5

that was you

[worthy summit]

yes

[soft thunder]

look here

but anyways

so you have your number 1, I told you to split it into 2 parts

[worthy summit]

yes

[soft thunder]

what was that again?

[worthy summit]

0.5

[soft thunder]

no

fractions

[worthy summit]

1/2

[soft thunder]

yes

[worthy summit]

IT WAS THAT ALL ALONG??

[soft thunder]

yes..

xD

[worthy summit]

omg im dumb

[soft thunder]

no this is a crucial step

please split the 1 into 519 parts now

write it as a fraction

[worthy summit]

1/519

[soft thunder]

now into a million parts

[worthy summit]

1/1000000

[soft thunder]

how would you go about restoring your shattered 1 now?

[worthy summit]

by reverting it back to the fraction

[soft thunder]

what mathematical operation would you need to do

on 1/1000000

to restore the 1

[worthy summit]

divide by 1 million

[soft thunder]

real quick

what is the opposite of -

[worthy summit]

posotive

[soft thunder]

I want to see a sign

[soft thunder]

what is the opposite of /

[worthy summit]

.

[soft thunder]

meaning?

[worthy summit]

decimal

[soft thunder]

have you not had multiplication and division yet?

[worthy summit]

i have

OHHHH

[soft thunder]

why is the opposite of dividing not multiplying then

[worthy summit]

my bad i didnt relize u meant division

[soft thunder]

how else would you visualize division

whatever

now that we established that

what do you need to get back your 1 that has been shattered into 1 million pieces?

[worthy summit]

multiply

[soft thunder]

by?

[worthy summit]

1000000

[soft thunder]

and what about the 1/519?

[worthy summit]

multiply by 519

[soft thunder]

what about the 1/2?

[worthy summit]

by 2

[soft thunder]

now

prize question

opposite/200m

[worthy summit]

multiply by 200

[soft thunder]

200m

but yes

[worthy summit]

yes

[soft thunder]

and since it is an equation

0.925 = opposite / 200m

you need to do it on both sides

[worthy summit]

so multiply by 2oom on both sides

200m*

[soft thunder]

you got it

[worthy summit]

0.925=185

and 200= 400

[soft thunder]

hey now

1 = 1

how can 200 = 400

[worthy summit]

oh so its still 200

[soft thunder]

look

let's take another little detour

1 = 1 right?

[worthy summit]

yes

[soft thunder]

if I tell you to multiply by 2, what does it have to look like?

[worthy summit]

2x1

[soft thunder]

you need to keep the equation

the = sign

[worthy summit]

wdym

[soft thunder]

well 1 = 1

now multiply by 2

[worthy summit]

2=2

[soft thunder]

yes

but in essence it would be 1x2 = 1x2

got it?

[worthy summit]

got it

[soft thunder]

now

0.925 = opposite / 200m

multiply by 200m

[worthy summit]

0.925x200=200x200?

[soft thunder]

where did the opposite go

[worthy summit]

0.925x200=Opposite x 200

[soft thunder]

let's go back to the 1/519

how do we reverse it?

[worthy summit]

multiply by 519

[soft thunder]

but we wouldn't have 1 x 519

we would just have 1

[worthy summit]

yes

[soft thunder]

how did we go from opposite / 200m to opposite x 200m then

[worthy summit]

cause id have to multiply by 200 both sides right

[soft thunder]

but only once on each side

of the = sign

you did it twice on the right side

[worthy summit]

so how do i do that with the division sign still there

[soft thunder]

remember 1/519?

[worthy summit]

yes

[soft thunder]

it's the same sign

you multiply by 519

to get rid of it

[worthy summit]

yes

[soft thunder]

same with the opposite / 200m

[worthy summit]

so i have to multiply 200 to get rid of it

[soft thunder]

you multiply by 200m to get rid of it

[worthy summit]

so would it be 185=opposite?

[soft thunder]

don't forget the units

but you got it

[worthy summit]

185m= opposite

[soft thunder]

yes

congrats you solved it

[worthy summit]

so thats the answer?

[soft thunder]

yep

[worthy summit]

wow, thank you so much

u really taught me a lot

thank you

[soft thunder]

I'm kinda suprised you pulled through this well

well done

[worthy summit]

lol i felt like i did bad

i got confused a lot

[soft thunder]

I think with a bit more practice you will get this in no time

[worthy summit]

i agree

[soft thunder]

we spent a few hours on this

and look where we are

[worthy summit]

i know haha

[soft thunder]

I would call this good progress

[worthy summit]

it really helped

me too

[soft thunder]

keep it up!

[worthy summit]

thank you!

thanks for being so patient

and thanks for your time as well

[soft thunder]

always a pleasure

if you are done you can close the ticket with .close I believe

[worthy summit]

okay thanks

you have a good rest of ur night or day

[soft thunder]

you too

[worthy summit]

.close