In the triangle ABC C = 90 º, BC = 6, tgB = 1/3. Find AB and AC.

The tangent of an acute angle in a right-angled triangle is the ratio of the opposite leg to the adjacent leg, that is, in our case, tg of the angle B = AC: CB, which is 1: 3 by condition.

Find AC, AC = (CB × 1): 3 = (6 × 1): 3 = 2;

Now let’s find AB. By the Pythagorean theorem, AC ^ 2 + CB ^ 2 = AB ^ 2;

4 + 36 = AB ^ 2;

AB = √40;

AB = 2√10;

Answer: AC = 2; AB = 2√10.