Triangle problem

We can use the Law of Cosines :

b^2  =a^2 + c^2  - 2(a)(c)cos(B)

b^2  = 58^2 + 24^2 - 2(58)(24) cos(64°)

b = sqrt [ 58^2 + 24^2 - 2(58)(24) cos(64°)] = about 52.15

Using the Law of Sines

sinC/ 24  = sin B / 52.15

sin C  / 24  = sin(64)/ 52.15

sin C =  24*sin(64)/ 52.15

sin^-1 [ 24* sin (64)/ 52.15]  = C  = about  24.43°

So   A  = [ 180 - 52.15 - 24.43]  = about  103.42°