In a right triangle, the hypotenuse is 10 and the acute angle is 30 degrees. Find the area of the triangle.

The cosine of an angle is the ratio of the leg adjacent to the given angle to the hypotenuse of the triangle.

This means that the leg a, adjacent to the angle equal to 30 °, can be found as the product of the hypotenuse and the cosine of the angle: a = 10 * cos 30 ° = 10 * √3 / 2 = 5√3.

The area of a triangle can be defined as half the product of two sides of a triangle multiplied by the sine of the angle between them: S = 0.5 * 10 * 5√3 * sin 30 ° = 0.5 * 10 * 5√3 * 0.5 ≈ 21, 65.