In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3:1. One of the angles of the triangle is

Let angle A = 3x (opposite BC = 2k) and angle B = x (opposite CA = k). By sine rule: 2k/sin3x = k/sinx, so sin3x = 2sinx. Using sin3x = 3sinx - 4sin³x: 3sinx - 4sin³x = 2sinx, sinx(1 - 4sin²x) = 0, so sin²x = 1/4, sinx = 1/2, x = 30°. So angle B = 30°.