By the law of sines:

k

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 =  

                             k =  

                             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