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

Nov 15, 2015

$L = 10 , h = 5 \sqrt{3}$

#### Explanation:

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

L is the hypotenuse, $\frac{L}{2} = 5$ is the short one, h is the long one.

Nov 15, 2015

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

#### Explanation:

${30}^{o}$-${60}^{o}$-${90}^{o}$ is a special kind of right-triangle in which sides exist in ratio $S L : L L : H = 1 : \sqrt{3} : 2$

where
$S L =$Short Leg,
$L L =$Long Leg,
$H =$Hypotenuse

The side-lengths can also be calculated with these relations
$S L = \frac{1}{2} H$ or $S L = \frac{1}{\sqrt{3}} L L$
$L L = \frac{\sqrt{3}}{2} H$ or $L L = S L \sqrt{3}$

Therefore, if $S L = 5$ in

$L L = 2 \sqrt{3} = 3.464$ in
and
$H = S L \times 2 = 5 \times 2 = 10$ in