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

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Answer 1 · 2015-11-21T02:26:15

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

![http://www.regentsprep.org/regents/math/algtrig/att2/ltri30.htm]( useruploads.socratic.org )

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

![https://commons.wikimedia.org]( useruploads.socratic.org )

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

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

$a \sqrt{3}$ $asqrt(3)$
$= 3 \sqrt{3}$ $=3sqrt(3)$

$2 a$ $2a$
$= 2 (3)$ $=2(3)$
$= 6$ $=6$