In a right-angled triangle, the angle is 30 °, and the smaller leg is 11 cm. Calculate the length of the hypotenuse.

1. A, B, C – the vertices of the triangle. ∠С = 90 °. ∠А = 30 °.

2. We calculate the degree measure of the angle ∠В:

180 ° – ∠А – ∠С = 180 ° – 30 ° – 90 ° = 60 °.

3. The BC leg is the smaller leg, as it is opposite the smaller angle. Less

the leg is equal by the condition of the problem to 11 centimeters. BC = 11 centimeters.

4. We calculate the length of the hypotenuse AB through the sine ∠A:

BC: AB = sine 30 ° = 1/2.

AB = BC: 1/2 = 11: 1/2 = 22 centimeters.

Answer: the length of the hypotenuse AB is 22 centimeters.