In triangle ABC, angle A = 50 degrees, angle B = 40 degrees, AB = 15cm and AC = 12cm. Find the BC side.

Find the angle C. Since the sum of the angles in the triangle is 180 degrees, we find the angle 180-50-40 = 90 degrees.
If the angle is 90 degrees, then the triangle is a rectangle and according to the Pythagorean theorem, you can find the leg CB.
Pythagorean theorem: the sum of the squares of the leg is equal to the square of the hypotenuse.
AB ^ 2-AC ^ 2 = CB ^ 2;
15 * 15-12 * 12 = 225-144 = 81 = CB ^ 2
CB = √81.
CB = 9.