A perpendicular CM is drawn through the vertex of the right angle C of the right-angled triangle ABC to its plane.

A perpendicular CM is drawn through the vertex of the right angle C of the right-angled triangle ABC to its plane. Find the length of the side AB of the triangle ABC if CM = 8 cm, BM = 17 cm, CAB = 30 degrees.

Consider a right-angled triangle BCM, in which the angle of the MCB is straight, since the CM is perpendicular to the plane of the triangle ABC.

Determine the length of the leg CB by the Pythagorean theorem CB ^ 2 = BM ^ 2 – CM ^ 2 = 17 ^ 2 – 8 ^ 2 = 289 – 64 = 225.

CB = 15 cm.

Consider a right-angled triangle ABC, in which the angle ACB = 90, and the angle CAB = 30.

Leg CB of a right triangle, opposite an angle of 300, is equal to half the length of the hypotenuse AB.

SV = AB / 2, then AB = 2 * SV = 2 * 15 = 30 cm.

Answer: Side AB = 30 cm.