An isosceles triangle with apex at 150 degrees and sides at 15. Find the area of the triangle.

Let us find the area of an isosceles triangle, if it is known:

Vertex = 150 °;

The sides are 15.

The area of any triangle is equal to half the product of the sides of the triangle and the sine of the angle between them.

We get:

S = 1/2 * 15 * 15 * sin 150 ° = 1/2 * 225 * sin 150 ° = 1/2 * 225 * sin (90 ° + 60 °) = 225/2 * cos 60 ° = 225/2 * 1/2 = 225 / (2 * 2) = 225/4 = 200/4 + 25/4 = 200/4 + 20/4 + 5/4 = 50 + 5 + 4/4 + 1/4 = 50 + 5 + 1 + 0.25 = 56 + 0.25 = 56.25.

From this we find that the area of an isosceles triangle is 56.25.

Answer: 56.25.