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.
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