An isosceles triangle ABC is given. Drawn perpendicular BH = 6 cm. Angle B = 120 degrees. Find AB.

1. Angle A is equal to angle B, as are the angles at the base of an isosceles triangle.

2. We calculate their value, based on the fact that the total value of the inner angles of the triangle is 180 °:

Angle A = Angle B = (180 ° – 120 °): 2 = 30 °.

3. In triangle ABH, leg BH is opposite an angle of 30 °. Consequently, its length is half the length of the hypotenuse AB.

4. Calculate the length of the hypotenuse AB:

AB = BH x 2 = 6 x 2 = 12 centimeters.

Answer: AB length is 12 centimeters.