The two sides of the triangle are 10 and 15 cm, and the angle between them is 60 degrees.

The two sides of the triangle are 10 and 15 cm, and the angle between them is 60 degrees. Find the third side of the triangle and its area.

The area of a triangle can be found as half the product of the lengths of its two sides by the sine of the angle between them:

S = 0.5 * a * b * sin α = 0.5 * 10 * 15 * sin 60 ° = 0.5 * 10 * 15 * √3 / 2 = 75√3 / 2 ≈ 64.95 cm2.

The third side is defined by the cosine theorem:

c ^ 2 = a ^ 2 + b ^ 2 – 2 * a * b * cos α = 10 ^ 2 + 15 ^ 2 – 2 * 10 * 15 * cos 60 ° = 100 + 225 – 150 = 175;

s = √175 = 5√7 ≈ 13.23 cm.