In triangle ABC, angle C is 90 degrees. BC = 4, Tg = 4/33.

It is known:

BC = 4;
tg A = 4 / √33.

To calculate the side AB of a right-angled triangle ABC with an angle of C = 90 degrees, we use the formula:

tg A = BC / AC;

AC = BC / tg A;

AC = 4 / (4 / √33) = 4/1 * √33 / 4 = 4/4 * √33 = 1 * √33 = √33;

Let’s find the side AB by the Pythagorean theorem.

AB = √ (AC ^ 2 + BC ^ 2) = √ (√33 ^ 2 + 4 ^ 2) = √ (33 + 16) = √49 = √7 ^ 2 = 7;

Answer: AB = 7.