Find the sum of the sides of an isosceles triangle with an apex angle of 120 if its height is 19.5 cm.

The height of an isosceles triangle divides it into two equal right-angled triangles. In this way:

AB = BC;

AH = НС, and they have a common side ВН.

The height of an isosceles triangle is also the bisector of the angle opposite the base and divides it in half:

∠AВН = ∠НВС = ∠ABС / 2;

∠АВН = ∠НВС = 120º / 2 = 60º.

Consider the triangle ΔАВН. Using the cosine theorem, we find the length of the side AB:

cos B = HВ / AB;

AB = BH / cos B;

cos 60º = 1/2 = 0.5;

AB = 19.5 / 0.5 = 39 cm.

AB + BC = 39 + 39 = 78 cm.

Answer: the sum of the sides of an isosceles triangle is 78 cm.