The shorter leg of a 30°-60°-90° triangle measures 3 inches. What is the length of the longer leg?

For a 30°-60°-90° triangle, the sides will have a ratio of 1:sqrt (3) : 2. Therefore if the shortest side (across the 30 ° angle) has a length ratio of 1, then the longer leg has a length ratio of sqrt (3). Therefore we have the proportion:

3 inches/1 = x/sqrt (3)

x = 3sqrt (3) inches

Note that the side of length ratio 2 is the hypotenuse, not the longer leg.