6. The longest side of a 30° -60° - 90° triangle measures 8. What is the length of the longer leg?

4x the square root of three. A 30 60 90 right triangles’ legs are in a ratio of sqrt3/2:1/2:1. Since 1 is the part of the ratio representing the longest side, and our longest side is 8, our new ratio for our 30,60 90 triangle is 4xsqrt3:4:8. Since 4xsqrt3 is the longest leg (leg of length 4 being the other), 4xsqrt3 is the longest leg