The angle opposite to the base of an isosceles triangle is 120 °. The height drawn to the side is 8 cm.

The angle opposite to the base of an isosceles triangle is 120 °. The height drawn to the side is 8 cm. Find the base of this triangle.

An isosceles triangle, given by condition, ABC (angle A = angle C = x). By the theorem on the sum of the angles of a triangle:
x + angle B + x = 180 degrees;
2x + 120 degrees = 180 degrees;
2x = 60 degrees;
x = 30 degrees.
angle A = angle C = x = 30 degrees.
A height AH = 8 cm is drawn from the corner A to the side BC.
Consider a triangle AНС – rectangular, since the height of AH is perpendicular to the side of the BC. Angle C = 30 degrees.
According to the properties of a right-angled triangle, opposite an angle of 30 degrees, a leg is 2 times smaller than the hypotenuse. Since the leg AH, which lies opposite an angle of 30 degrees, is 8 cm, the hypotenuse of AC (also the base of the ABC triangle) will be equal to 2 * AH = 2 * 8 = 16 (cm)
Answer: 16 cm