The two sides of the triangle are 5cm and 7cm and the angle between them is 60º find the third side of the triangle.

According to the cosine theorem, the square of the side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of these sides by the cosine of the angle between them.

We will assume that AC = 5 cm, AB = 7 cm, it is necessary to find the side BC.

BC ^ 2 = AC ^ 2 + AB ^ 2 – 2 * AC * AB * cos 60 ° = 5 ^ 2 + 7 ^ 2 – 2 * 5 * 7 * 0.5 = 25 + 49 – 35 = 39.

BC = √39 cm.

Answer: the third side of the triangle is √39 cm.