In a triangle, the two sides are 15 cm and 16 cm, and the angle between them is 120 degrees
| May 5, 2021 | education
In a triangle, the two sides are 15 cm and 16 cm, and the angle between them is 120 degrees. find the third side of the triangle.
According to the cosine theorem, the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of these sides by the cosine of the angle between them:
a ^ 2 = b ^ 2 + c ^ 2 – 2 * b * c * cos α.
The square of the unknown side of this triangle is:
a ^ 2 = 15 ^ 2 + 16 ^ 2 – 2 * 15 * 16 * cos 120 = 225 + 256 – 480 * (-0.5) = 721.
The desired side is equal to:
a = √721 ≈ 26.85 cm.
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