# In a 30-60-90 triangle, the shorter leg has length of 8sqrt3 m. What is the length of the other leg (L) and the hypotenuse?

Nov 26, 2015

height = $24$
hypotenuse = $16 \sqrt{3}$

#### Explanation:

In the diagram above, the shortest length is represented by the variable $a$. The other lengths are multiples of $a$.

If $a = 8 \sqrt{3}$:

$a \sqrt{3}$
$= \left(8 \sqrt{3}\right) \sqrt{3}$
$= 24$

$2 a$
$= 2 \left(8 \sqrt{3}\right)$
$= 16 \sqrt{3}$

$\therefore$, the height is $24$ and the hypotenuse is $16 \sqrt{3}$.