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

Nov 15, 2015

The length of longer leg$= 8.487$

#### 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
$S L =$Shorter Leg,
$L L =$Longer Leg,
$H =$Hypotenuse

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

Therefore, if $H = 9.8$

$L L = \frac{\sqrt{3}}{2} \times 9.8 = 8.487$