In triangle ABC, angle C = 90 degrees, AB = 3√17, AC = 3. Find tgA -?

The legs in the triangle will be AC and BC, and the hypotenuse will be AB.

Opposite corner A, leg BC will be located. We find its length by the Pythagorean theorem:

ВС = √ (AB ^ 2 – AC ^ 2) = √ ((3√17) ^ 2 – 3 ^ 2) = √ (9 * 17 – 9) = √ (9 * (17-1)) = 3 * 4 = 12.

The tangent is found as the ratio of the BC leg to the AC leg (opposite to the adjacent angle):

Answer: tg A = 4/12 = 1/3.