Using the cosine theorem, find all the angles of a triangle if the sides are: a = 14, b = 18, c = 20.

univerkov | March 17, 2021 | education

By the cosine theorem, we determine the value of the angle ACB.

AB ^ 2 = BC ^ 2 + AC ^ 2 – 2 * BC * AC * CosACB.

400 = 196 + 324 – 2 * 14 * 18 * CosACB.

504 * CosACB = 120.

CosACB = 120/504 = 0.238.

Angle ACB = arcos (0.238) ≈ 760 10 ‘.

By the cosine theorem, we determine the value of the angle ABC.

AC ^ 2 = BC ^ 2 + AB ^ 2 – 2 * BC * AB * CosABC.

324 = 196 + 400 – 2 * 14 * 20 * CosACB.

560 * CosABC = 272.

CosABC = 272/560 = 0.486.

Angle ABC = arcos (0.486) ≈ 610 4 ‘.

Then the angle BAC = 180 – ACB – ABC = 180 – 760 10 ‘- 610 4’ = 420 46 ‘.

Answer: The angles of the triangle are equal: 760 10 ‘, 610 4’, 420 46 ‘.

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