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

July 28, 2021 | education

| **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.

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