In a triangle ABC, the angle is C = 90 degrees, BC = 6 cm, tgB = 1/3. Find AB and AC.

1. We calculate the length of the leg AC through the tangent ∠B – the ratio of the leg opposite the specified angle (opposite) to the leg, which is the side of this angle (adjacent):

AC / BC = tangent ∠B = 1/3.

AC = 6/3 = 2 centimeters.

2. Calculate the length AB – the hypotenuse of a given triangle using the formula of the theorem

Pythagoras:

AB = √BC² + AC² = √6² + 2² = √36 + 4 = √40 = 2√10 cm.

Answer: AB = 2√10 centimeters, AC = 2 centimeters.