The two sides of the triangle are equal to 7 and 8 cm, and the angle between them is 120 graus, find the third side.

We find the third side by the cosine theorem.

c ^ 2 = a ^ 2 + b ^ 2 – 2ab * cosγ.

By condition, a = 7 cm, b = 8 cm, γ = 120.

c ^ 2 = 7 ^ 2 + 8 ^ 2 – 2 * 7 * 8 * cos (120) = 49 + 64 – 112 * cos (180-60) = 113 – 112 * (-cos (60)) =

113 + 112 * 1/2 = 113 + 56 = 169.

c ^ 2 = 169.

c = 13 or c = -13.

According to the condition of the problem, it was necessary to find the length of the side of the triangle, and it cannot be negative. Therefore, c = -13 does not satisfy the condition of the problem.

Answer: 13 cm.