Final answer:
The length of the longer leg of the 30°-60°-90° triangle is 8√3 inches.
Step-by-step explanation:
The length of the longer leg of the 30°-60°-90° triangle can be found using the ratios of the sides. In a 30°-60°-90° triangle, the ratio of the longer leg to the hypotenuse is √3 : 2. Therefore, the length of the longer leg can be found by multiplying the length of the hypotenuse by √3/2:
Length of longer leg = 16 inches * √3/2 = 8√3 inches