In triangle ABC, angle C = 90 degrees, AB = 208, AC = 80. Find the tangent A.

univerkov | August 9, 2021 | education

Since C = 90 °, the triangle is right-angled. Find the leg CB, by the Pythagorean theorem we get:

BC ^ 2 = AB ^ 2 – AC ^ 2 = 208 ^ 2 – 80 ^ 2 = 43264 – 6400 = 36864;

BC = √36864 = 192.

Then:

tg (A) = AC / BC = 80/192 = 5/12.

Answer: The tangent of angle A is 5/12.

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