Given: triangle ABC angle C = 90 ° angle B = 60 ° AB + BC = 12 cm Find: AB and BC.

Let us determine what value the angle A in our figure will equal if from the condition of our problem we know for sure that the other two angles are equal to 60 ° and 90 °, respectively:

180 – 90 – 60 = 30.

Opposite the angle found above is the BC side, and as we know from the school curriculum, it is equal to half the hypotenuse, that is, the AB side.

Let BC be equal to a.

Then AB can be expressed as 2a.

Since we know that their sum is 12 cm, then we write down the equation and find them:

2a + a = 12;

3a = 12;

a = 4;

4 * 2 = 8.

Answer: BC = 4 cm, AB = 8 cm.