# In a 30-60-90 triangle, where the shortest leg equals 3, what could the other sides equal?

Nov 21, 2015

The lengths of the other sides are $6$ and $3 \sqrt{3}$.

#### Explanation:

In the diagram above, the side length $1$ is the shortest side.

Similarly, in this diagram, you would substitute 3 as your shortest side. So, $a = 3$

To find the lengths of the other two sides, substitute $a = 3$ into $a \sqrt{3}$ and $2 a$:

$a \sqrt{3}$
$= 3 \sqrt{3}$

$2 a$
$= 2 \left(3\right)$
$= 6$