anonymous
  • anonymous
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Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
Ok how does angle C equal 20 and PS is 5?
anonymous
  • anonymous
Unkle it's not that hard come on...

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UnkleRhaukus
  • UnkleRhaukus
there are 360° in a complete revolution, angle C is 1 eighteenth of the wayround \[\angle C=360°/18\]
anonymous
  • anonymous
wait what so how its it 20 on there?
UnkleRhaukus
  • UnkleRhaukus
did you simplify \(\angle C =\frac{360°}{18}=\dots\)
anonymous
  • anonymous
ohhh
UnkleRhaukus
  • UnkleRhaukus
\[36=2\times18\] \[360=2 \times 18\times10\]
anonymous
  • anonymous
How would you find the area?
UnkleRhaukus
  • 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
  • UnkleRhaukus
|dw:1338432746562:dw|
anonymous
  • anonymous
ok wait
anonymous
  • anonymous
I have a diferent problem on my notes.. Same shape but it says each side = 4
anonymous
  • anonymous
What is the area.
anonymous
  • anonymous
|dw:1338433164896:dw|
anonymous
  • anonymous
like that
UnkleRhaukus
  • UnkleRhaukus
you can find length CS = a using a trigonometric function of the angle 20°
anonymous
  • anonymous
Lets say the question only give you the length of one side is 4
anonymous
  • anonymous
How would you go about finding the area?
UnkleRhaukus
  • UnkleRhaukus
|dw:1338432905847:dw|
anonymous
  • anonymous
|dw:1338433361442:dw|
anonymous
  • 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
  • anonymous
Half of one side is 2.
UnkleRhaukus
  • UnkleRhaukus
\[\tan(20°)=\frac{\text{opposite}}{\text{adjacent}}=\frac5a\] \[a=\frac 5{\tan(20°)}\neq4\]
UnkleRhaukus
  • UnkleRhaukus
or is the 4 coming from a different problem/
UnkleRhaukus
  • UnkleRhaukus
the diagram posed at the top of the page does not have any side- length equal to 4
anonymous
  • anonymous
4 from a different problem
UnkleRhaukus
  • UnkleRhaukus
OK, what is the new problem exactly/
anonymous
  • anonymous
What I drew that's all it gives me
anonymous
  • anonymous
A decagon with a side lengths of 4. Find the Area.
UnkleRhaukus
  • UnkleRhaukus
well the first one was a nonagon so the picture is wrong
anonymous
  • anonymous
RAWRRRRRRRRR I HATE MATH SO MUCH OMFG
UnkleRhaukus
  • UnkleRhaukus
|dw:1338433609250:dw|
anonymous
  • anonymous
I DONT HAVE TIME FOR THISSSS I WANNA SLEEP
anonymous
  • anonymous
Yes now find the area. Just with that information.
UnkleRhaukus
  • UnkleRhaukus
well should i sing you a lullaby instead ?
anonymous
  • anonymous
LOL
UnkleRhaukus
  • 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
  • UnkleRhaukus
next find the length of the perpendicular , using the angle you just found and the tangent function
UnkleRhaukus
  • 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
  • anonymous
360/10 =36? When I apply the TAN to 36 it's weird...
anonymous
  • anonymous
@UnkleRhaukus
UnkleRhaukus
  • UnkleRhaukus
true, what did you determine as an approximation of length b
UnkleRhaukus
  • UnkleRhaukus
2 significant figures is probably fine
anonymous
  • anonymous
huh? I didnt get that far becuase I thought you need to know the TAN of 36
anonymous
  • anonymous
@satellite73
UnkleRhaukus
  • UnkleRhaukus
yeah \[\tan(36°)\approx0.727\]
anonymous
  • anonymous
ok.. Let me see
UnkleRhaukus
  • UnkleRhaukus
\[\tan(36°)=\frac{\text{opp}}{\text{adj}}=\frac 2 b\] \[b=\frac {2}{\tan36°}\approx\cdots\]
anonymous
  • anonymous
why is it b= 2/tan36?
anonymous
  • anonymous
Ohh I got it
anonymous
  • anonymous
so its 2.75
UnkleRhaukus
  • 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
  • UnkleRhaukus
yes \(b\approx 2.75\)
anonymous
  • 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
  • UnkleRhaukus
find the area of this triangle |dw:1338435087210:dw|
UnkleRhaukus
  • UnkleRhaukus
\[A_{\triangle}=\frac{ab}2=\frac {2b}2=\cdots\]
UnkleRhaukus
  • UnkleRhaukus
you dont need the perimeter
anonymous
  • anonymous
My notes has it O.o
anonymous
  • anonymous
Maybe hes teaching it like that?
anonymous
  • anonymous
THe formula for Area is. 1/2 * Apothem * perimeter
UnkleRhaukus
  • 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
  • anonymous
Yeah lol same thing I got.
anonymous
  • anonymous
Well, thanks for taking like 30 minutes of your time to help me lol.
anonymous
  • anonymous
I'm so dumb.

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