In an isosceles triangle, one of the angles is 120 degrees, and the side is 16 cm. Find the height drawn to the base.

An isosceles triangle is a triangle in which the sides are equal.

The height of an isosceles triangle is also the bisector of the angle at the vertex ∠B, and also divides this triangle into two equal right-angled triangles.

In order to find the height of the ВН, consider the triangle AВН.

∠AВН = ∠ABС / 2;

∠AВН = 120º / 2 = 60º.

To calculate the height of the ВН, we apply the cosine theorem. The cosine of an acute angle of a right triangle is the ratio of the adjacent roll to the hypotenuse:

cos B = BH / AB;

BH = AB · cos B;

cos 60º = 1/2;

BH = 16 ∙ 1/2 = 16/2 = 8 cm.

Answer: The length of the HВ height is 8 cm.