Question

The hypotenuse of a 30-60-90 triangle measures start fraction, 2, divided by, square root of, 3, end square root, end fraction
3
​

2
​
inches. What is the length of the longer leg?

Answer 1

In a 30-60-90 triangle the sides are in the ratio 1 : √3 : 2 (short leg : long leg : hypotenuse). If the hypotenuse is H, the longer leg = (√3/2)H.

With H = 2/√3,
longer leg = (√3/2)·(2/√3) = 1.

So the longer leg is 1 inch.