In triangle ABC, angle B is 120 degrees, median BM halves angle B and is equal to 21. Find AB.

Let us determine the degree value of the angle ABM, knowing by the condition of the problem, the median BM divides into two equal parts the angle B of the triangle ABC, the degree value of which is 120 °:

120: 2 = 60.

Since, according to the condition of the problem, the median BM is also a bisector, the triangle ABC is isosceles, which means that it is also a height. Therefore triangle ABM is rectangular.

Determine how many centimeters the length AB is equal to, knowing that cos 60 ° is 1/2:

21: 1/2 = 42.

Answer: Length AB is 42 centimeters.