In an isosceles triangle ABC with a base AC, the angle B = 120 cm

In an isosceles triangle ABC with a base AC, the angle B = 120 cm, and the height drawn from the vertex B = 13 cm find: the sides of the triangle

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 apex ∠B, and also divides this triangle into two equal right-angled triangles.

In order to find the length of the lateral side AB, consider the triangle ΔАВН.

∠AВН = ∠ABС / 2;

∠АВН = 120º / 2 = 60º.

To calculate AB, we apply the cosine theorem. The cosine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse:

cos B = ВН / AB;

AB = BH / cos B;

cos 60º = 1/2 = 0.5;

AB = 13 / 0.5 = 26 cm.

Since in this triangle the sides are equal, then:

BC = AB = 26 cm.

Answer: the sides of the triangle are 26 cm.