In triangle ABC, angle B = 90, BC = 5, tgC = 2.4. Find the AC.

Find AC in triangle ABC.

It is known:

Angle B = 90 °;
BC = 5;
tg C = 2.4.
Decision:

In this triangle, AC = hypotenuse, AB and BC are legs.

tg C = BC / AB.

From here we find leg AB.

AB = BC / tg C;

AB = 5 / 2.4 = 5 / (2 4/10) = 5 / (2 2/5) = 5 / (12/5) = 5/1 * 5/12 = 1/12;

Let’s find AC by the Pythagorean theorem.

AC = √ (AB ^ 2 + BC ^ 2) = √ ((1/12) ^ 2 + 5 ^ 2) = √ (1/144 + 25) = √ (1 + 25 * 144) / √144 = √ (3601/144) = √3601 / 12;

As a result, we got that the hypotenuse of the triangle is AC = √3601 / 12.