In triangle ABC, angle C is 90 BC = 1 tgA = 1 / √3 find AB.

Explanation: The tangent of the angle is equal to the ratio of the opposite leg to the adjacent leg.

tgA = 1 / √3;

tgA = CB / AC;

1 / √3 = 1 / AC;

AC = √3 cm;

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = AC ^ 2 + BC ^ 2;

AB ^ 2 = (√3) ^ 2 + 1 ^ 2;

AB ^ 2 = 4;

AB = 2 cm.

Answer: 2 centimeters.