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 a triangle if its area is 1089.

A triangle is three points that do not lie on one straight line, connected by segments. In this case, the points are called the vertices of the triangle, and the segments are called its sides.

An isosceles triangle is a triangle in which the sides are equal.

In order to find the side of a triangle, we use the formula for the area through two sides and the angle between them:

S = 1/2 * a * b * sin α, where:

a, b – sides of the triangle;

α is the angle between them.

Since the triangle is isosceles, then:

a = b.

Thus:

S = 1/2 * a2 * sin α;

sin 30º = 1/2 = 0.5;

a ^ 2 = S / (sin α ∙ 1/2);

a ^ 2 = 1089 / (0.5 * 0.5) = 1089 / 0.25 = 4356;

a = √4356 = 66 cm.

Answer: the length of the side of the triangle is 66 cm.