SOLUTION: the sum of the sides of a triangle ABC is 200m.If angle A=37,B=59,and C=84,find the side opposite the biggest angle.

Algebra ->  Angles -> SOLUTION: the sum of the sides of a triangle ABC is 200m.If angle A=37,B=59,and C=84,find the side opposite the biggest angle.      Log On


   

Question 716016: the sum of the sides of a triangle ABC is 200m.If angle A=37,B=59,and C=84,find the side opposite the biggest angle.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
By the law of sines:

a%2Fsin%28A%29%22%22=%22%22b%2Fsin%28B%29%22%22=%22%22c%2Fsin%28C%29%22%22=%22%22k

Therefore

 a = k·sin(A), b = k·sin(B), c = k·sin(C)

                     a + b + c = 200

Substituting:

k·sin(A) + k·sin(B) + k·sin(C) = 200

Factor out k

  k·[sin(A) + sin(B) + sin(C)] = 200

Solve for k
                             k = 200%2F%28sin%28A%29%2Bsin%28B%29%2Bsin%28C%29%29 

                             k = 200%2F%28sin%28%2237%B0%22%29%2Bsin%28%2259%B0%22%29%2Bsin%28%2284%B0%22%29%29 

                             k = 81.51606116

 a = k·sin(A),     b = k·sin(B),     c = k·sin(C)
 a = k·sin(37°),   b = k·sin(59°),   c = k·sin(84°)
 a = 49.05759024m, b = 69.87290211m, c = 81.06950765m

You just wanted c = 81.06950765m

Edwin