Angle ABC = 120 degrees. From point A, the perpendicular AMK of the straight line BC is drawn. Find BM if AB = 18.

According to the condition, the angle ABC = 120 °, and from point A, a perpendicular AM K of the straight line BC is drawn. This means that point M will be outside the triangle ABC (CM> CB).

Consider triangle AMB.

In it, we know that the angle AMB = 90 °, and the side AB, which is the hypotenuse of the triangle AMB, is equal to 18.

It is also easy to find the AVM angle. It is equal to 180 ° – angle ABC = 180 ° – 120 ° = 60 °.

Since the angle ABM = 60 °, the angle BMA = 30 °.

This means that, by the property of a right-angled triangle, the leg lying opposite an angle of 30 ° is equal to half of the hypotenuse, i.e. BM = 1/2 * AB = 1/2 * 18 = 9.

Answer: ВM = 9.