Find the area of a triangle ABC if: AB = 12, AC = 8, angle A = 30 °.

There are several ways to calculate the area of a triangle. One way is this: the product of adjacent sides is multiplied by 0.5 and multiplied by the sine of the angle between the adjacent sides taken. In our problem, the lengths of two adjacent sides and the angle between them are known. Let’s find the area of a triangle by the formula:

S = 0.5 * AB * AC * sin A;

S = 0.5 * 12 * 8 * sin A;

S = 0.5 * 96 * sin A;

S = 48 * sin A;

A = 30 °;

Sin A = sin 30 ° = 1/2 = 0.5;

S = 48 * 1/2;

S = 24 cm².

Answer: the area of the triangle ABC is 24 cm².