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?

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Answer 1 · 2015-11-26T03:34:18

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)#.