## anonymous one year ago PLEASE HELP: MEDAL AND FAN Solve the triangle. A = 51°, b = 11, c = 7

1. anonymous

@campbell_st

2. anonymous

can you help? @swamijatin2

3. swamijatin2

what we have to find perimeter or area

4. anonymous

neither

5. anonymous

lol wrong thing sorry

6. anonymous

I need a (side a); C(angle c); and B(angle b)

7. anonymous

@campbell_st

8. anonymous

ok

9. swamijatin2

or well that doesnt have to be a right triangle but

10. anonymous

now what

11. anonymous

@satellite73

12. anonymous

how do i do this

13. anonymous

draw a triangle that looks reasonably like this one then use the law of cosines

14. anonymous

i have a triangle but how do i use the law of cosines (i know what it is just not how to do it)

15. anonymous

$a^2=b^2+c^2-2bc\cos(A)$ $a^2=11^2+7^2-2\times 11\times 7\cos(51^\circ)$ and a calculator

16. swamijatin2

To solve the traingle we need to find remaining side a and angles B and C. Use law of cosines a2 = b2 + c2 - 2bc cosA a2 = (11)2 + (7)2 - 2(11)(7) cos(51) a2 = 121 + 49 - 154 cos(51) a2 = 170 - 154(0.629) a2 = 170 - 96.866 a2 = 73.134 a = 8.55

17. anonymous

i got that ok so how about the and C

18. anonymous

B and C angles

19. swamijatin2

Now use law of sines sinA/a = sinB/b sin(51)/ 8.55 = sin(B)/11 sin(B) = 11[sin(51)/ 8.55] sin(B) = 11[0.777/8.55] B = sin-1(0.999) B = 87.43°

20. anonymous

ok and C?

21. swamijatin2

Sum of angles in triangle = 180° A + B + C = 180 C = 180 - (A + B) C = 180 - (51 + 87.43) C = 180 - 138.43 C = 41.57°

22. anonymous
23. anonymous

because none of those are my answers

24. swamijatin2

then you are incorrect anywhere

25. anonymous

what?

26. swamijatin2

27. anonymous

8.5 is a which is only for one answer choice where B = 85.9 and C = 39.1

28. anonymous

a ≈ 12.8, C ≈ 39.1, B ≈ 89.9 a ≈ 8.5, C ≈ 39.1, B ≈ 89.9 No triangles possible a ≈ 12.8, C ≈ 43.1, B ≈ 85.9

29. swamijatin2

you r correct but according to question we have to do

30. anonymous

@Loser66

31. anonymous

32. anonymous

@phi

33. anonymous

we have done a lot but it doesn't match my answer choices

34. phi

can you re-post the question and the answer you got? It would take a long time to read through all of the posts up above.

35. anonymous

sure hold on

36. anonymous

Solve the triangle. A = 51°, b = 11, c = 7

37. anonymous

Work From above: a2 = b2 + c2 - 2bc cosA a2 = (11)2 + (7)2 - 2(11)(7) cos(51) a2 = 121 + 49 - 154 cos(51) a2 = 170 - 154(0.629) a2 = 170 - 96.866 a2 = 73.134 a = 8.55 Now use law of sines sinA/a = sinB/b sin(51)/ 8.55 = sin(B)/11 sin(B) = 11[sin(51)/ 8.55] sin(B) = 11[0.777/8.55] B = sin-1(0.999) B = 87.43° Sum of angles in triangle = 180° A + B + C = 180 C = 180 - (A + B) C = 180 - (51 + 87.43) C = 180 - 138.43 C = 41.57°

38. anonymous

My answer choices are: a ≈ 12.8, C ≈ 39.1, B ≈ 89.9 a ≈ 8.5, C ≈ 39.1, B ≈ 89.9 No triangles possible a ≈ 12.8, C ≈ 43.1, B ≈ 85.9

39. anonymous

so... what do we do?

40. phi

side a is correct. a= 8.55 redo your work for angle B

41. phi

the problem is when you do the work for angle B, you need lots of decimals of accuracy. for side a, don't round it to 8.55. use all the digits your calculator has.

42. anonymous

ok

43. phi

it might be more accurate to first find angle C sin C = (7*sin51)/8.548956649

44. anonymous

what do you get for angle B i got the same answer

45. anonymous

I got 0.63633750 Radians for C?

46. phi

sin C = 0.63633750 C= asin( 0.63633750 ) = 39.519 deg

47. phi

summarizing a= 8.55, b= 11, c= 7 A= 51, B= 89.5, C= 39.5 the best match to your choices is choice B

48. phi

if we use a=8.6 (round from 8.55) we would get C= 39.2 and B= 89.8 which is even closer to choice B.

49. phi

because they use ≈ which means approximately it is reasonable to pick choice B. And the other choices are not "in the ball park"