In the ABC Triangle, the angle C is 90 degrees, AC = 6, tg A = √7 / 3. Find AB.

univerkov | September 15, 2021 | education

The tangent of an acute angle in a right-angled triangle is the ratio of the opposite leg to the adjacent one;
tg A = √ 7/3 = BC / AC;
ВС = AC ∙ tg А = 6 ∙ √ 7/3 = 2 √ 7;
Then, by the Pythagorean theorem:
AB = √ (BC² + AC²) = √ (6² + 4 ∙ 7) = √ 64 = 8;
Answer: AB = 8;

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