In triangle ABC, angle C is 90∘, tgA = 2√4, BC = 4. Find AB.

In triangle ABC it is known:

Angle C = 90 °;

tg A = 2√4;

BC = 4.

Find the hypotenuse AB of the right-angled triangle ABC.

1) First, find the AC leg.

tg A = BC / AC;

From here we will express AC.

AC = BC / tg A;

Substitute the known values.

AC = 4 / (2√4) = 2 / √4 = 2/2 = 1;

2) By the Pythagorean theorem, we find the hypotenuse AB.

AB = √ (AC ^ 2 + BC ^ 2) = √ (1 ^ 2 + 4 ^ 2) = √ (1 + 16) = √17.

Hence, AB = √17.