Solve a triangle with a = 32. b = 38, and c = 46.

A. A = 43.5°: B = 54.8°: C = 81.70

B. A = 54.3º: B = 54.8°; C = 81.70

C. A = 43.5°: B = 66.5°; C = 81.7

D. A = 43.50: B = 54.8°; C = 78.4°

Using the law of cosines:

Angle A

a^2 = b^2 + c^2 - 2 * b * c * cos (Angle A)

32^2 = 38^2 + 46^2 - 2 * 38 * 46 * cos (Angle A)

1024 = 1444 + 2116 - 3496 * cos (Angle A)

3496 * cos (Angle A) = 1444 + 2116 - 1024

3496 * cos (Angle A) = 2536

cos (Angle A) = 2536 / 3496

Angle A = arccos (2536 / 3496)

Angle A = 43.5 degrees.

Using the same steps calculate angle b and angle c (rearrange the formula to have b^2 and c^2 equal to:

Angle b = 54.8 degrees

Angle C = 81.7 degrees.

The answer is A. A = 43.5°: B = 54.8°: C = 81.70