Question

In a 30°-60°-90° triangle, the length of the hypotenuse is 30. Find the length of the longer leg.

Answer 1

In a 30-60-90  triangle the side opposite the 30 degree angle is half the length of the hypotenuse. 
The shorter leg is the side opposite the 30 degree angle, therefore
the shorter leg = 30/2 = 15

By the Pythagorean theorem
the longer leg = √(30² - 15²) = √(900-225) = √675 = 15√3 ≈ 25.98 units