Find the area of an isosceles triangle if its side is 6 and its base angle is 15 degrees.

We have an isosceles triangle. Two known values are also given – the side and the angle at the base:
a = 6 cm.
A = 15 °.
Let’s find the area of the triangle.
The area of a triangle will be found by applying a formula with a half-product of the values of the two sides and the angle between them.
We have two sides – two sides. It remains to find the angle between them.
As you know, the sum of the angles of a triangle is 180 °. The angles at the base are equal, which means that the angle between the side vertices is:
180 ° – 2 * 15 ° = 150 °.
Then the area is:
S = 1/2 * a * a * sin 150 ° = 1/2 * 36 * 1/2 = 9 cm².