1). Triangle ABC is a right triangle with angle B = 60 degrees and side AB = 10 cm. Find the length of side BC.

Solution:

1. We are given a right triangle ABC, with angle C = 90 degrees, angle B = 60 degrees, and the hypotenuse AB = 10 cm.
2. We need to find the length of side BC.
3. We can use the cosine function, which is defined as the ratio of the adjacent side to the hypotenuse in a right triangle: cos(B) = BC / AB.
4. Rearranging the formula to solve for BC, we get: BC = AB * cos(B).
5. Substituting the given values: BC = 10 cm * cos(60 degrees).
6. The cosine of 60 degrees is 0.5.
7. Therefore, BC = 10 cm * 0.5 = 5 cm.

Ответ: 5 см