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

September 23, 2021 | education

| **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.

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