In a right-angled triangle ABC, the angle is B = 90, CB = 15cm, cosC = 3: 5. Find CA and AB.

By definition, the cosine of an angle in a right-angled triangle is the ratio of the leg adjacent to this angle to the hypotenuse. In this example, the adjacent leg CB is 15 cm, and the cosine of angle C is 3/5. Therefore, we find the hypotenuse CA from the relation

cosC = CB / CA;

CA = CB / cosC = 15 / (3/5) = 25 cm.

Knowing the length of one of the legs and the hypotenuse of a right triangle, we find the length of the second leg using the Pythagorean theorem:

AB = √ (CA ^ 2 – CB ^ 2) = √ (25 ^ 2 – 15 ^ 2) = √ (625 – 225) = √ (400) = 20 cm.