In triangle abc, angle c = 90 degrees cosA = 0.2 BC = 4√6 find AB.

univerkov | April 11, 2021 | education

Let’s define the tangent of the angle BAC through its cosine.

tg2BAC = (1 / Cos2BAC) – 1 = (1 / 0.04 – 1) = 25 – 1 = 24.

tgBAC = 2 * √6.

TgBAC = BC / AC.

AC = BC / tgBAC = 4 * √6 / 2 * √6 = 2 cm.

Then AB = √ (AC2 + BC2) = √ (4 + 96) = 10 cm.

Answer: The length of the hypotenuse AB is 10 cm.

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