In a 30-60-90 triangle, the shorter leg has length of ##8sqrt3## m. What is the length of the other leg (L) and the hypotenuse?

height = ##24## hypotenuse = ##16sqrt(3)##

In the diagram above, the shortest length is represented by the variable ##a##. The other lengths are multiples of ##a##.

If ##a=8sqrt(3)##:

##asqrt(3)## ##=(8sqrt(3))sqrt(3)## ##=24##

##2a## ##=2(8sqrt(3))## ##=16sqrt(3)##

##:.##, the height is ##24## and the hypotenuse is ##16sqrt(3)##.