## AcidRa1n 3 years ago Picture

1. AcidRa1n

2. AcidRa1n

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

3. AcidRa1n

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

4. UnkleRhaukus

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

5. AcidRa1n

wait what so how its it 20 on there?

6. UnkleRhaukus

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

7. AcidRa1n

ohhh

8. UnkleRhaukus

$36=2\times18$ $360=2 \times 18\times10$

9. AcidRa1n

How would you find the area?

10. 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

11. UnkleRhaukus

|dw:1338432746562:dw|

12. AcidRa1n

ok wait

13. AcidRa1n

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

14. AcidRa1n

What is the area.

15. AcidRa1n

|dw:1338433164896:dw|

16. AcidRa1n

like that

17. UnkleRhaukus

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

18. AcidRa1n

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

19. AcidRa1n

How would you go about finding the area?

20. UnkleRhaukus

|dw:1338432905847:dw|

21. AcidRa1n

|dw:1338433361442:dw|

22. AcidRa1n

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.

23. AcidRa1n

Half of one side is 2.

24. UnkleRhaukus

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

25. UnkleRhaukus

or is the 4 coming from a different problem/

26. UnkleRhaukus

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

27. AcidRa1n

4 from a different problem

28. UnkleRhaukus

OK, what is the new problem exactly/

29. AcidRa1n

What I drew that's all it gives me

30. AcidRa1n

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

31. UnkleRhaukus

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

32. AcidRa1n

RAWRRRRRRRRR I HATE MATH SO MUCH OMFG

33. UnkleRhaukus

|dw:1338433609250:dw|

34. AcidRa1n

I DONT HAVE TIME FOR THISSSS I WANNA SLEEP

35. AcidRa1n

Yes now find the area. Just with that information.

36. UnkleRhaukus

well should i sing you a lullaby instead ?

37. AcidRa1n

LOL

38. 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 $360°/10$

39. UnkleRhaukus

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

40. UnkleRhaukus

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

41. AcidRa1n

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

42. AcidRa1n

@UnkleRhaukus

43. UnkleRhaukus

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

44. UnkleRhaukus

2 significant figures is probably fine

45. AcidRa1n

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

46. AcidRa1n

@satellite73

47. UnkleRhaukus

yeah $\tan(36°)\approx0.727$

48. AcidRa1n

ok.. Let me see

49. UnkleRhaukus

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

50. AcidRa1n

why is it b= 2/tan36?

51. AcidRa1n

Ohh I got it

52. AcidRa1n

so its 2.75

53. 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 $$\tan36°$$

54. UnkleRhaukus

yes $$b\approx 2.75$$

55. AcidRa1n

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

56. UnkleRhaukus

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

57. UnkleRhaukus

$A_{\triangle}=\frac{ab}2=\frac {2b}2=\cdots$

58. UnkleRhaukus

you dont need the perimeter

59. AcidRa1n

My notes has it O.o

60. AcidRa1n

Maybe hes teaching it like that?

61. AcidRa1n

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

62. 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 $$A_{decagon}=2.752\times20=\cdots$$

63. AcidRa1n

Yeah lol same thing I got.

64. AcidRa1n

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

65. AcidRa1n

I'm so dumb.