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)##.

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