The two sides of the triangle are 5 cm and 7 cm, and the angle between them is = 60 degrees.

The two sides of the triangle are 5 cm and 7 cm, and the angle between them is = 60 degrees. Find the third side of the triangle.

From the current school curriculum, we well know that the square of the side of a triangle will be calculated as the sum of the squares of the other two sides minus the doubled product of these sides and the cosine of the angle that lies between them.

Let us determine what the unknown side of the triangle will equal, when from the condition of the task we know that the other two sides are 5 and 7 cm, respectively, the angle between them is 60 °

x 2 = 5 ^ 2 + 7 ^ 2 – 2 * 5 * 7 * 1/2 = 39;

x1 = √39;

x2 = -√39 (not suitable).

Answer: √39 cm.