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

March 23, 2021 | education

| **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.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.