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- anonymous

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- Stacey Warren - Expert brainly.com

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- anonymous

##### 1 Attachment

- anonymous

Ok how does angle C equal 20 and PS is 5?

- anonymous

Unkle it's not that hard come on...

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## More answers

- UnkleRhaukus

there are 360° in a complete revolution, angle C is 1 eighteenth of the wayround
\[\angle C=360°/18\]

- anonymous

wait what so how its it 20 on there?

- UnkleRhaukus

did you simplify \(\angle C =\frac{360°}{18}=\dots\)

- anonymous

ohhh

- UnkleRhaukus

\[36=2\times18\]
\[360=2 \times 18\times10\]

- anonymous

How would you find the area?

- UnkleRhaukus

well the shape can be see as 18 of those little right angled triangle joined together,
find the area of one then multiply by 18

- UnkleRhaukus

|dw:1338432746562:dw|

- anonymous

ok wait

- anonymous

I have a diferent problem on my notes.. Same shape but it says each side = 4

- anonymous

What is the area.

- anonymous

|dw:1338433164896:dw|

- anonymous

like that

- UnkleRhaukus

you can find length CS = a
using a trigonometric function of the angle 20°

- anonymous

Lets say the question only give you the length of one side is 4

- anonymous

How would you go about finding the area?

- UnkleRhaukus

|dw:1338432905847:dw|

- anonymous

|dw:1338433361442:dw|

- anonymous

Thats all it gives you. Find the area. I know it has something to do with finding the apothem and finding the perimeter and using the TAN function.

- anonymous

Half of one side is 2.

- UnkleRhaukus

\[\tan(20°)=\frac{\text{opposite}}{\text{adjacent}}=\frac5a\]
\[a=\frac 5{\tan(20°)}\neq4\]

- UnkleRhaukus

or is the 4 coming from a different problem/

- UnkleRhaukus

the diagram posed at the top of the page does not have any side-
length equal to 4

- anonymous

4 from a different problem

- UnkleRhaukus

OK, what is the new problem exactly/

- anonymous

What I drew that's all it gives me

- anonymous

A decagon with a side lengths of 4. Find the Area.

- UnkleRhaukus

well the first one was a nonagon so the picture is wrong

- anonymous

RAWRRRRRRRRR I HATE MATH SO MUCH OMFG

- UnkleRhaukus

|dw:1338433609250:dw|

- anonymous

I DONT HAVE TIME FOR THISSSS I WANNA SLEEP

- anonymous

Yes now find the area. Just with that information.

- UnkleRhaukus

well should i sing you a lullaby instead ?

- anonymous

LOL

- UnkleRhaukus

ok so you might want to find the angle in triangle first,
remember there are 360° in a revolution and i count 10 angles,
so the angle in is \[360°/10\]

- UnkleRhaukus

next find the length of the perpendicular , using the angle you just found and the tangent function

- UnkleRhaukus

|dw:1338433908040:dw|, find the area of the triangle and lastly multiply this area by the number of those triangles in the decagon

- anonymous

360/10 =36? When I apply the TAN to 36 it's weird...

- anonymous

@UnkleRhaukus

- UnkleRhaukus

true, what did you determine as an approximation of length b

- UnkleRhaukus

2 significant figures is probably fine

- anonymous

huh? I didnt get that far becuase I thought you need to know the TAN of 36

- anonymous

@satellite73

- UnkleRhaukus

yeah \[\tan(36°)\approx0.727\]

- anonymous

ok.. Let me see

- UnkleRhaukus

\[\tan(36°)=\frac{\text{opp}}{\text{adj}}=\frac 2 b\]
\[b=\frac {2}{\tan36°}\approx\cdots\]

- anonymous

why is it b= 2/tan36?

- anonymous

Ohh I got it

- anonymous

so its 2.75

- UnkleRhaukus

we are trying to find \(b\) so we can work out the are of the triangle \[\tan(36°)=\frac{\text{opp}}{\text{adj}}=\frac 2 b\]
multiply both sides by \(b\)
then divide both sides by \(\tan36°\)

- UnkleRhaukus

yes \(b\approx 2.75\)

- anonymous

so then after we find the area which is 2.752 we take the perimeter which is 40, and do 1/2* 2.752* 40

- UnkleRhaukus

find the area of this triangle |dw:1338435087210:dw|

- UnkleRhaukus

\[A_{\triangle}=\frac{ab}2=\frac {2b}2=\cdots\]

- UnkleRhaukus

you dont need the perimeter

- anonymous

My notes has it O.o

- anonymous

Maybe hes teaching it like that?

- anonymous

THe formula for Area is. 1/2 * Apothem * perimeter

- UnkleRhaukus

whatever, my method is better ~
so the area of the small right angled triangle is 2.752
and there are 20 of these in the decagon
the the total area is simply \(A_{decagon}=2.752\times20=\cdots\)

- anonymous

Yeah lol same thing I got.

- anonymous

Well, thanks for taking like 30 minutes of your time to help me lol.

- anonymous

I'm so dumb.

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