In triangle ABC, angle C = 90 degrees, angle A = 15 degrees, BC = 11cm. Point M was marked on the leg AC

In triangle ABC, angle C = 90 degrees, angle A = 15 degrees, BC = 11cm. Point M was marked on the leg AC so that the angle BMC = 30 degrees. Find the segment AM.

BCM triangle – rectangular with angles 90 °, 30 ° and 60 °;

In a right-angled triangle with such degree measures of angles, the hypotenuse is always twice the leg, which forms an angle of 60 ° with the hypotenuse, therefore:

BM = BC * 2 = 11 * 2 = 22 cm;

The ABM triangle turned out to be isosceles, since the angles A = ABM = 15 °;

lateral sides of an isosceles triangle BM = AM = 22 cm.