In a right-angled triangle ABC: angle C = 90 degrees, BC = 3cm, cos angle B = 0.6. Find AB, AC.

1. Taking into account that, according to the properties of a right-angled triangle, the ratio of the leg BC and the hypotenuse AB is equal to the cosine of this angle, we calculate the length of the hypotenuse AB:

BC / AB = cosine of angle B = 0.6.

AB = 3 / 0.6 = 5 centimeters.

2. Using the Pythagorean theorem, we calculate the length of the AC leg:

AC = √AB ^ 2 – BC ^ 2 = √5 ^ 2 – 3 ^ 2 = √25 – 9 = √16 = 4 centimeters.

Answer: the length of the hypotenuse AB is 5 centimeters, the length of the AC leg is 4 centimeters.