In a triangle ABC, the angles A B C are 1: 2: 3. Find the length BC if AB = 12.

Let the angle BAC = X0, then the angle ABC = 2 * X0, the angle ACB = 3 * X0.

The sum of the interior angles of a triangle is 180.

Then X + 2 * X + 3 * X = 180.

6 * X = 180.

X = 180/6 = 30.

Angle BAC = 30, angle ABC = 60, angle ACB = 90, which means triangle ABC is rectangular.

The BC leg lies opposite the angle 30, then its length is equal to half the length of the hypotenuse AB.

BC = AB / 2 = 12/2 = 6 cm.

Answer: The length of the BC side is 6 cm.