In triangle ABC, angle C is 90 degrees; angle B is 60 degrees. CB is 3cm. Find AB.

Since the angle ∠С in this triangle is equal to 90º, this triangle is right-angled. Thus, to calculate the length of the hypotenuse AB, it is most convenient to apply the cosine theorem. The cosine of an acute angle of a right triangle is the ratio of the adjacent leg to the hypotenuse:

cos B = BC / AB;

AB = BC / cos B;

cos 60º = 1/2 = 0.5;

AB = 3 / 0.5 = 6 cm.

Answer: the length of the hypotenuse AB is 6 cm.