In a 30-60-90 triangle, where the long leg is 12, what is the length of the short leg?

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Answer 1 · 2015-11-15T19:10:50

The length of short leg#=6.928#

#30^o#-#60^o#-#90^o# is a special kind of right-triangle in which sides exist in ratio #SL:LL:H = 1:sqrt(3):2#

where
#SL=#Short Leg,
#LL=#Long Leg,
#H=#Hypotenuse

The side-lengths can also be calculated with these relations
#SL=1/2H# or #SL=1/sqrt3LL#
#LL=sqrt3/2H# or #LL=SLsqrt3#

Therefore, if #LL=12#

#SL=1/sqrt3xx12=4sqrt3=6.928#