Calculate the third side of a triangle if its two sides are respectively 5 cm and 2 cm, and the angle between them is 120 °.
| July 11, 2021 | education
Using the cosine theorem, we find the third side of the triangle, we have:
c ^ 2 = 5 ^ 2 + 2 ^ 2 – 2 * 5 * 2 * cos120˚ = 5 ^ 2 + 2 ^ 2 – 2 * 5 * 2 * cos (180˚ – 60˚) = 5 ^ 2 + 2 ^ 2 + 2 * 5 * 2 * cos60˚ = 25 + 4 + 20 * (1/2) = 29 + 10 = 39.
c = √39 (cm) or c = -√39 – does not satisfy the condition of the problem.
Answer: the third side of the triangle is √39 cm.
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