In a right-angled triangle, one of the legs is 10, and the acute angle adjacent to it is 30. Find the area of the triangle.

x – opposite leg.

Knowing that the tangent of angle A is the ratio of the opposite leg x to the adjacent a, we define the opposite leg x.

tg A = x / a;

x = tg 300 * a.

Using the Bradis tables, we determine tg 300 = 0.5774.

x = 0.5774 * 10 = 5.8.

Determine the area of the triangle.

S = a * x / 2;

S = 10 * 5.8 / 2;

S = 58/2;

S = 29 square units.

Answer: the area of the triangle S = 29 square units.