In triangle ABC, side AB = 4 cm, angle A = 30 °, angle B = 45 °. Find side AC.

The AC side we need is located opposite the corner B. This by the condition side AB is located opposite the corner C.
To solve the problem, we use the theorem of sines. We write down the ratio of the sides to the sines of the opposite angles and get the proportion.
AB / sin C = AC / sin B;
AC = AB * sin 45 ° / sin 30 ° = 4 * √2 / 2 / 1/2 = 4√2 (cm).
Answer: the AC side is 4√2 cm.