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

1 Answer
Nov 15, 2015

The length of short leg=6.928

Explanation:

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