One of the legs in a right-angled triangle is 15 cm, and the tangent of the adjacent corner is 1.5 cm

One of the legs in a right-angled triangle is 15 cm, and the tangent of the adjacent corner is 1.5 cm. Find the length of the second leg.

Given: AC = leg; AC = 15 centimeters; BC – leg; tgA = 1.5.

Find: Cathet BС.

Let’s write down the definition of the tangent:

Tangent is the ratio of the opposite leg to the adjacent one.

This means that AC is the adjacent leg, and BC is the opposite (in relation to the hypotenuse AB).

Let us write down the relation emerging from the definition of the tangent and the conditions of the problem:

BC / AC = tgA.

Let’s substitute the data from the condition into this relation:

BC / 15 = 1.5;

Now from this formula we can derive the formula for finding the unknown BC leg. Let’s deduce:

BC = 15 * 1.5;

BC = 22.5 centimeters.

Answer: BC = 22.5 centimeters.