In triangle ABC, angle C = 90 degrees, tg of angle A is 0.75, AB = 15cm Find the perimeter of the triangle.

univerkov | April 5, 2021 | education

Determine the cosine of the angle BAC.

Cos2BAC = 1 / (1 + tg2BAC) = 1 / 1.5625 = 0.64.

CosBAC = 0.8.

Then AC = AB * CosBAC = 15 * 0.8 = 12 cm.

SinBAC = √ (1 – 0.64) = 0.6.

Then BC = AB * SinBAC = 15 * 0.6 = 9 cm.

Rasv = AB + BC + AC = 15 + 9 + 12 = 36 cm.

Answer: The perimeter is 36 cm.

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