In the ABC triangle, the angle is A = 90 degrees, the outer angle at the vertex is B = 150 degrees.

In the ABC triangle, the angle is A = 90 degrees, the outer angle at the vertex is B = 150 degrees. Find CB and AC if the difference between these sides is 10 cm.

In a triangle ABC <A = 90; <B = 180 ° – 150 ° = 30 °; then the hypotenuse BC = 2 * (AC), since the AC leg is opposite the angle <B = 30 °.

Then, taking the value BC = a; AC = a / 2, we write down their value according to the condition: a – a / 2 = 10 cm, whence a / 2 = 10 cm, a = 2 * 10 cm = 20 cm.

Check: a = 20 cm, a / 2 = 10 cm, their difference (a – a / 2) = a / 2 = 10 cm.