In triangle ABC, angle C is 90 *, AB = 10, AC = 8. Find tgA.

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

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

tg A = BC / AC.

To do this, we will find the length of the opposite leg of the BC. We apply the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BC ^ 2 + AC ^ 2;

BC ^ 2 = AB ^ 2 – AC ^ 2;

BC ^ 2 = 10 ^ 2 – 8 ^ 2 = 100 – 64 = 36;

BC = √36 = 6 cm.

tg A = 6/8 = 3/4 = 0.75.

Answer: the tangent of the angle ∠A is 0.75.