In triangle ABC, angle C is 90 degrees. AB = √181, AC = 10. Find tg A.

In this triangle AB is the hypotenuse, AC is the leg adjacent to angle A, BC is the leg opposite to angle A.

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

tg A = BC / AC

Let us find the BC from the ABC triangle according to the Pythagorean theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

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

BC ^ 2 = AB ^ 2 – AC ^ 2;

BC ^ 2 = (√181) ^ 2 – 10 ^ 2 = 181 – 100 = 81; BC = 9.

tg A = BC / AC = 9/10.

Answer. 9/10.