The two sides of the triangle are exactly 6 cm and 4 cm, and the angle between them is

The two sides of the triangle are exactly 6 cm and 4 cm, and the angle between them is -120 degrees. Find the length of the third side of the triangle.

1) How long is the third side of the triangle?

Using the cosine theorem, we find the third side of the triangle, we have:

c ^ 2 = 6 ^ 2 + 4 ^ 2 – 2 * 6 * 4 * cos120˚ = 62 + 42 – 2 * 6 * 4 * cos (180˚ – 60˚) = 6 ^ 2 + 4 ^ 2 + 2 * 6 * 4 * cos60˚ = 36 + 16 + 48 * (1/2) = 52 + 24 = 76.

c = √76 = 2√19 (cm) or c = -√76 = -2√19 – does not satisfy the condition of the problem.

Answer: the third side of the triangle is 2√19 cm.