In triangle ABC, angle C is 90 degrees AC = 5.6 tangent of A 24/7, find AB.

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

tg A = 24/7;

tg A = BC / AC;

BC / AC = 24/7;

BC / 5.6 = 24/7;

7 * BC = 5.6 * 24;

7 BC = 134.4;

BC = 19.2 cm.

Let’s find the hypotenuse of a triangle according to the Pythagorean theorem (the sum of the squares of the legs is equal to the square of the hypotenuse):

AC² + BC² = AB²;

5.6² + 19.2² = AB²;

31.36 + 368.64 = AB²;

AB² = 400;

AB = √400;

AB = 20 cm – triangle hypotenuse

Answer: 20 cm