In a triangle ABC, the angle is C = 90 degrees, AB = 8√5, AC = 8. find tg A.

univerkov | August 19, 2021 | education

The first way.

By the Pythagorean theorem, we determine the length of the BC leg.

BC ^ 2 = AB ^ 2 – AC ^ 2 = 320 – 64 = 256.

BC = 16 cm.

Then tgBAC = BC / AC = 16/8 = 2.

Second way.

In a right-angled triangle ABC CosBAC = AC / AB = 8/8 * √5 = 1 / √5.

Then Sin2BAC = 1 – Cos2BAC = 1 – 1/5 = 4/5.

SinBAC = 2 / √5.

tgBAC = SinBAC / CosBAC = (2 / √5) / (1 / √5) = 2.

Answer: The tangent of the angle BAC is 2.

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