In triangle ABC, angle C = 90 degrees AB = 10 tg angle A = 0.75 Find AC.

A triangle in which one angle is 90º is called rectangular.

To calculate the length of the AC leg, it is most convenient to use the cosine theorem.

The cosine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse:

cos A = AC / AB;

AC = AB ∙ cos A.

Find cos A.

Since the tangent of the angle ∠A is 0.75, then:

0.75 = tg 37º;

cos 37º ≈ 0.8;

AC = 10 ∙ 0.8 = 8 cm.

Answer: the length of the AC leg is 8 cm.