The hypotenuse of a 30°-60°-90° triangle is 30. What is the length of one of its legs?

In a 30°-60°-90° triangle, the sides are in the ratio 1:√3:2. The longest side (hypotenuse) is opposite the 90° angle, the shortest side is opposite the 30° angle, and the remaining side is opposite the 60° angle.

Given that the hypotenuse is 30, we can use the ratios to find the lengths of the other sides.

1. The side opposite the 30° angle (the shortest side) is half the length of the hypotenuse. So, its length is 30/2 = 15.

2. The side opposite the 60° angle (the remaining side) is √3 times the length of the shortest side. So, its length is 15*√3.

Therefore, the lengths of the legs of the triangle are 15 and 15√3.