Question

The sides of an isosceles triangle are 8, 8, and 3. The measure of the vertex angle to the nearest degree is _____°.

Answer 1

We may draw a vertical that bisects the vertex angle and the shorter side of the triangle, to form a right-triangle with the measurements:

hypotenuse = 8

length = 1.5

We may then apply:

sin(∅) = P / H

sin(∅) = 1.5 / 8

∅ = 10.8 ≈ 11°

This is half of the vertex angle, so the vertex angle is:

11 * 2 = 22°