Find the area of a right-angled triangle with a hypotenuse of 6 and an angle of 15∘.

The solution of the problem:

1. Let’s define the smaller leg (k1).

sin150 = k1: 6;

k1 = sin150 * 6;

k1 = 0.26 * 6;

k1 = 1.56.

2. Let’s define the larger leg (k2).

k22 = 62 – 1.562;

k22 = 36 – 2.43;

k2 = √33.57;

k2 = 5.79.

3. Determine the area of the triangle.

S = 1/2 * k1 * k2;

S = 1/2 * 1.56 * 5.79;

S = 9.03: 2;

S = 4.52.

Answer: The area of a triangle is 4.52 square units.