Given a triangle ABC. BC = 8, AC = 9, angle C = 30 degrees. Find the area of this triangle.

Let’s find the area of a triangle using the formula, when the length of the two sides and the angle between them are known:

S = 1/2 * a * b * sinα, where a is the side of the triangle, b is the side of the triangle,

α is the angle between sides a and b. In our example, a = BC, b = AC.

Substitute the data and find the area of the triangle:

S = 1/2 * 8 * 9 * sin30 = 18 cm2

Answer: the area of the triangle is 18 cm2.