Find the perimeter of a triangle, the two sides of which are 21 cm and 24 cm, and the angle between them is 120 °.

In this case, you need to use the cosine theorem, which says that the square of the side of a triangle is equal to the sum of the squares of the other two sides, from which you need to subtract the product of these sides by the cosine of a given angle.

Thus, we find the third side of the triangle (C):

C = √ (a² + b² – 2ab * cos120) = √ (21² + 24² – 2 * 21 * 24 * (-1 / 2)) = 39 (cm);

Now we find the perimeter of the triangle by adding all the sides:

21 + 24 + 39 = 84 (cm)

Answer: 84 cm.