In a right-angled triangle ABC with right angle A, side BC is 12 cm and angle B is 60 degrees. Find side AB.

To solve the problem, we use the following properties of a right-angled triangle:

1) the sum of the acute angles is 90 “;

2) the leg opposite to the 30 “angle is equal to half of the hypotenuse.

In ∆ABC ∟A = 90 “, then AB and AC are legs, BC is hypotenuse.

So, ∟ В + ∟С = 90 “, then ∟С = 90” – 60 “= 30”. And the leg AB is opposite to the angle C, which means AB = BC: 2 = 6 (cm).