In a 30-60-90 triangle, what is the length of the long leg and hypotenuse if the short leg is 5 in long?

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Answer 1 · 2015-11-15T19:04:09

#L = 10, h = 5 sqrt 3#

You have half an equilateral triangle of sides #(L ; L/2 ; h = L sqrt 3/2) #

L is the hypotenuse, #L/2 = 5# is the short one, h is the long one.

Answer 2 · 2015-11-15T19:40:36

Length of long leg#=3.464# in, Length of hypotenuse#=10# in

#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 #SL=5# in

#LL=2sqrt3=3.464# in
and
#H=SLxx2=5xx2=10# in