In a 30-60-90 triangle with a hypotenuse of length 9.8, what is the length of the longer of the two legs?

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Answer 1 · 2015-11-15T19:27:36

The length of longer leg#=8.487#

#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=#Shorter Leg,
#LL=#Longer Leg,
#H=#Hypotenuse

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

Therefore, if #H=9.8#

#LL=sqrt3/2xx9.8=8.487#