In the ABC triangle, the angle is C = 90 degrees, AB = 40, AC = 32. Find tgA

univerkov | August 28, 2021 | education

According to the Pythagorean theorem, in the right-angled triangle ABC, we determine the length of the leg BC.

BC ^ 2 = AB ^ 2 – AC ^ 2 = 1600 – 1024 = 576.

BC = 24 cm.

Then tgBAC = BC / AC = 24/32 = 0.75.

Second way.

Determine the cosine of the angle BAC.

CosBAC = AC / AB = 32/40 = 0.8.

Determine the sine of the angle BAC.

Sin2BAC = 1 – Cos2BAC = 1 – 0.64 = 0.36.

SinBAC = 0.6.

Then tgBAC = SinBAC / CosBAC = 0.6 / 0.8 = 0.75.

Answer: The tangent of the angle BAC is 0.75.

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