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
