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