In a triangle ABC, the angle is C = 90 °. AB = 5, tan B = 4/3. Find BC.

1. It is known that the tangent is the ratio of the opposite leg to the adjacent one.

In a triangle ABC, tgB = AC / BC = 4/3.

Let us express the sides of the AC and BC in parts.

AC = 4 parts, BC = 3 parts.

2. By the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs.

In triangle ABC

AB ^ 2 = BC ^ 2 + AC ^ 2 = 3 ^ 2 + 4 ^ 2 = 9 + 16 = 25;

5 cm = 25 ^ 1/2 = 5 pieces.

1 cm = 1 piece.

Found that one part of the sides AC and BC is equal to 1 centimeter.

3. Let’s calculate what the BC leg is.

BC = 1 cm * 3 = 3 cm.

Answer: The BC side of the ABC triangle is 3 centimeters.