SOLUTION: in triangle ABC, a = 5, b = 9, and c = 6. Find angle A, angle B, and angle C. Thanks

Algebra ->  Trigonometry-basics -> SOLUTION: in triangle ABC, a = 5, b = 9, and c = 6. Find angle A, angle B, and angle C. Thanks      Log On


   

Question 43785: in triangle ABC, a = 5, b = 9, and c = 6. Find angle A, angle B, and angle C.
Thanks
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
in triangle ABC, a = 5, b = 9, and c = 6
Use Law of Cosines:
a%5E2+=+b%5E2+%2B+c%5E2+-+2bc%28cos%28A%29%29
%28-a%5E2+%2B+b%5E2+%2B+c%5E2%29%2F%282bc%29+=+cos%28A%29
%28-5%5E2+%2B+9%5E2+%2B+6%5E2%29%2F%282%2A9%2A6%29+=+cos%28A%29
%28-25+%2B+81+%2B+36%29%2F%28108%29+=+cos%28A%29
%2892%29%2F%28108%29+=+cos%28A%29
cos%5E%28-1%29%2892%2F108%29+=+A
32+=+A
Use Law of Sines:
Sin%28A%29%2Fa+=+Sin%28B%29%2Fb
Sin%2832%29%2F5+=+Sin%28B%29%2F9
9%2ASin%2832%29%2F5+=+Sin%28B%29
sin%5E%28-1%29%289%2ASin%2832%29%2F5%29+=+B
73+=+B
Use Law of Sum of Interior Angles: 180%28b+-+2%29 : 180(3 - 2) : 180
180 - (32 + 73) = C
180 - 105 = C
75 = C