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

30-60-90 triangles are a special kind of right triangle in which the hypotenuse is twice as long as the shortest side, and the second longest side (the side opposite the 60 degree angle) is the product of the length of the shortest side and the square root of 3. If you know the length of any of the sides of a 30-60-90 triangle, you can easily find the other two side lengths.

Shortest side (side opposite the 30 degree angle) : a

Second shortest side (side opposite the 60 degree angle) : a√3

Hypotenuse (longest side; side opposite the 90 degree angle) : 2a

The hypotenuse is given, and the length of the longer leg is needed. To find the length of the longer leg, first find the length of the shorter leg.

Remember, the hypotenuse is twice the length of the short leg, thus the short leg of this triangle is half of thirty, or fifteen units.

The long leg is the product of the short leg and the square root of three. The long leg is 15√3.

Answer:

The longer leg is 15√3 units or approximately 26 units.