In an isosceles triangle, the side, equal to 32 cm, makes an angle of 75 degrees with the base.

In an isosceles triangle, the side, equal to 32 cm, makes an angle of 75 degrees with the base. Find the area of the triangle.

Since the triangle is isosceles, the angles at the base are equal and in this case are 75 degrees.

The angles of a triangle add up to 180 °

Hence the angle between the sides:

180 ° – 75 ° * 2 = 30 °

The area of a given triangle is calculated as half the product of these sides multiplied by the sine of the angle between them:

1/2 * (32 * 32 * sin (30 °)) = 1/2 * (32 * 32 * 1/2) = 256

Answer: the area is 256 cm²