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

2 Answers
Nov 15, 2015

L = 10, h = 5 sqrt 3L=10,h=53

Explanation:

You have half an equilateral triangle of sides (L ; L/2 ; h = L sqrt 3/2) (L;L2;h=L32)

L is the hypotenuse, L/2 = 5L2=5 is the short one, h is the long one.

Nov 15, 2015

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

Explanation:

30^o30o-60^o60o-90^o90o is a special kind of right-triangle in which sides exist in ratio SL:LL:H = 1:sqrt(3):2SL:LL:H=1:3:2

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

The side-lengths can also be calculated with these relations
SL=1/2HSL=12H or SL=1/sqrt3LLSL=13LL
LL=sqrt3/2HLL=32H or LL=SLsqrt3LL=SL3

Therefore, if SL=5SL=5 in

LL=2sqrt3=3.464LL=23=3.464 in
and
H=SLxx2=5xx2=10H=SL×2=5×2=10 in