The two sides of the triangle are 11cm and 24cm, and the angle between them is 120 °. Find the third side of the triangle.

1. The theorem of cosines is known: the square of the side of an arbitrary triangle is equal to the sum of the squares of the other two sides minus the double product of these sides by the cosine of the angle between them.

2. Find the AC side if AB is 11 centimeters, BC is 24 centimeters and B is 120 degrees.

cos120 degrees = – 1/2.

AC = (AB ^ 2 + BC ^ 2 – 2 * AB * BC * cosB) ^ 1/2 = (11 ^ 2 + 24 ^ 2 + 2 * 11 * 24 * 1/2) ^ 1/2 = (121 + 576 + 264) ^ 1/2 = 1061 ^ 1/2 = 32.57 centimeters.

Answer: The AC side of the ABC triangle is 32.57 centimeters.