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

March 30, 2021 | education

| 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.

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