Given a triangle ABC Angle C = 90 degrees Cosine B = 0.6 CB = 6 cm. Find AB AC.

1. The hypotenuse AB of the right-angled triangle ABC is found from the definition of the trigonometric function: the cosine of an acute angle is the ratio of the adjacent leg to the hypotenuse.

In a given triangle cos B = BC: AB.

By the condition of the problem, cos B = 0.6, CB = 6 cm.

So the required value is AB = BC: cos B = 6 cm: 0.6 = 10 cm.

2. The second leg of the AC is calculated by the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the legs, that is

AB² = AC² + BC² and then AC = √AB² – BC² = √10² – 6² = √100 – 36 = √64 = 8 cm.