In triangle ABC, angle C = 90 degrees, angle B = 60 degrees, CB = 6 cm. What is side AB?

A triangle is three points that do not lie on one straight line, connected by segments. These points are called the vertices of the triangle, and the line segments are called its sides.

If in a triangle at least one of the angles is 90º, then such a triangle is right-angled. The side opposite to the right angle is called the hypotenuse, and the other two are called the legs.

In order to find the length of the hypotenuse AB, it is most convenient to use the cosine theorem. The cosine of an acute angle of a right-angled 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 = 6 / 0.5 = 12 cm.

Answer: the length of the hypotenuse AB is 12 cm.