Find the hypotenuse of triangle ABC if angle B = 60 degrees BC = 5 cm.

Given: ABC is a right-angled triangle, angle B = 60 °, BC = 5 cm.

Find: hypotenuse AB =? cm.

Solution: 1) By the theorem, the sum of all angles in any triangle is 180 °.

So angle A + angle B + angle C = 180 °.

In a right-angled triangle ABC, angle C is 90 °, substitute this value and another angle B from the condition and get:

angle A + 60 ° + 90 ° = 180 °,

angle A = 180 ° – 150 °,

angle A = 30 °.

2) According to the theorem, in a right-angled triangle, a leg lying opposite an angle of 30 ° is equal to half of the hypotenuse. In our triangle opposite the angle A = 30 ° lies the leg BC = 5 cm.This means the hypotenuse AB = 5 * 2 = 10 cm.

Answer: AB = 10 cm.