In triangle ABC, angle A is 90∘, tgB = √3 / 3, AC = 5. Find BC.

In triangle ABC it is known:

Angle A is 90 °;
tg B = √3 / 3;
AC = 5.
Find BC.

Since the angle c = 90 °, it means that AB is the hypotenuse, AC and BC are the legs.

tg b = AC / BC;

Hence, ВС = AC / tg b;

Substitute the known values into the formula and calculate the value of the BC leg.

ВС = 5 / (√3 / 3) = 5/1 * 3 / √3 = 5 * 3 / √3 = 15 / √3 = 15 * √3 / 3 = 15/3 * √3 = 5√3;

As a result, we got that the leg of the triangle BC = 15√3.