In the triangle ABC, the angle C is 90 degrees BC = 20, AB = 4, the root of 34, find the tangent of the angle B.

It is known that the tangent is a function of the angle, equal in a right-angled triangle to the ratio of the leg, which lies opposite a given acute angle, to the adjacent leg.

In accordance with the condition in a right-angled triangle ABC (angle C = 90 degrees), the side BC is the adjacent leg, and the opposite leg AC can be calculated by the Pythagorean theorem as

AC ^ 2 = AB ^ 2 – BC ^ 2.

Thus, AC ^ 2 = (4 * (34) ^ (1/2) ^ 2 – 20 ^ 2 = 144 = 12 ^ 2.

So, BC = 20, AC = 12, and

the required value tg В = АС / ВС = 12/20 = 3/5.