Given: triangle ABC, AB = 8cm, AC = 6cm, angle C = 45 degrees. Find angle B.

To begin with, we draw a triangle ABC, in which we denote the angle C = 45 °, as well as the side of the AC, which, by condition, is 6 cm, and the side AB, which is 8 cm.
Since the unknown angle B lies against the AC side, and the known angle C against the AB side, we find the angle B through the theorem of sines: where sin B = 6/8 * sin C = 3/8 * √2, then the angle B is 32 °.