The angle at the apex opposite to the base of an isosceles triangle is 30 degrees.

The angle at the apex opposite to the base of an isosceles triangle is 30 degrees. Find the side of the triangle if its area is 529.

Let’s use the formula to calculate the area S of a triangle along two sides and the angle between them:

S = 1/2 a * b sin (C).

Since this triangle is isosceles and the angle between the sides is 30 °, then its area:

S = 1/2 * a * a * sin (30 °) = 1/2 * a ^ 2 * 1/2 = 1/4 * a ^ 2 = 529,

1/4 * a ^ 2 = 529,

a ^ 2 = 4 * 529,

a = 2 * 23 = 46.

Answer: the side is 46.