## anonymous one year ago If the length of an arc is 12 inches and the radius of the circle is 10 inches, what is the measure of the arc? 216 degrees 270 degrees 288 degrees

1. anonymous

2. wampominater

do you still need help?

3. anonymous

4. wampominater

ok

5. wampominater

so, the first thing you need is the formula for arc length, which is $arclength = 2piR(\frac{ \theta }{ 360 })$

6. wampominater

now, look at the values you are given

7. wampominater

you have the arc length and the radius, so plug those in.

8. wampominater

and what do you get when you do that?

9. anonymous

where am i plugging the arc length into?

10. wampominater

look at the formula, see where it says arc length? you plug the value you have for arc length right there.

11. anonymous

yeah and i can plug in the radius too. but what am i solving for?|dw:1438157454848:dw|

12. wampominater

yep! now you want to solve for theta.

13. anonymous

theta?

14. wampominater

so to make it easier, replace theta with x. it is the symbol in the numerator of the fraction: $\theta$

15. anonymous

oh okay.

16. wampominater

so the first step is to isolate x, the best way to do that is to first deal with everything outside the parenthesis

17. wampominater

you know all the values for those, just solve 2πr

18. wampominater

and then, what you want to do is divide both sides by the value that you get for 2πr, which will isolate the fraction and let you solve that next

19. anonymous

62.8?

20. wampominater

yep!

21. wampominater

now divide both sides by 62.8

22. wampominater

what do you get?

23. anonymous

okay |dw:1438157770787:dw| now divide by it?

24. wampominater

mhm, so it would be 12 over 62.8

25. wampominater

that leaves you with $\frac{ 12 }{ 62.8 } = \frac{ x }{ 360 }$

26. wampominater

now, go ahead and divide 12 by 62.8, what does that get you?

27. anonymous

couldnt you do that as a proportion?

28. wampominater

yes, you could if you like

29. anonymous

seems easier

30. anonymous

|dw:1438157995138:dw|

31. wampominater

yep! so that would be the answer i believe.

32. anonymous

isnt right

33. wampominater

hmm, let me see if i did something wrong

34. anonymous

yeah man

35. wampominater

hmm, im not sure what I did Wrong, sorry :(

36. anonymous

|dw:1438158390561:dw|

37. anonymous

@aric200

38. UsukiDoll

actually there is a dupe question and that also led to a dead end http://openstudy.com/study#/updates/52eafc6ae4b0d95ca6b32d90

39. wampominater

hmm, could be the question then? idk if you looked at the work usuki, is it right?

40. anonymous

its supposed to be 12 pi and copy paste takes out the pi part

41. UsukiDoll

I think the question is a bit screwed up... yes ! 12 pi that's what we need

42. wampominater

there we go! lol

43. wampominater

ok so then, it is 12π and not 12?

44. UsukiDoll

because that's also a dupe question http://openstudy.com/study#/updates/4e2c15f60b8b3d38d3ba2d2d

45. anonymous

yep

46. wampominater

alright, do you need help still then or are you good?

47. anonymous

so its 216?

48. UsukiDoll

I don't know if I should touch on this.. if there's a duplicate question. why not look at the past and learn in the future?

49. wampominater

good point, i didnt look :p

50. wampominater

yes it is 216

51. UsukiDoll

I could go over it for verification purposes so given radius at 10 ( r = 10) Arc length is 12pi (s=12pi) we need theta $s = \theta r \rightarrow \frac{s}{r} = \theta$ $\frac{12 \pi}{10} = \theta$ that bad boy is in radians and we need degrees so multiply that 12pi/10 with 180/pi so the pi's cancel $\frac{12 \pi}{10} \cdot \frac{180}{\pi} = \theta$ $\frac{12 }{10} \cdot \frac{180}{1} = \theta$ $\frac{2160}{10} = \theta$ $216 = \theta$

52. anonymous

what would be the symbol/variable for arc length?

53. UsukiDoll

arc length is s radius is r angle is the theta

54. wampominater

Alright, well thanks for the Help @UsukiDoll , ill be more careful in the future. goodnight!