Question 858520
If the angles are 30-60-90 and the sides opposite 
these angles are a, b, and c, then you know that
the sides are in these proportions:
a : {{{ 1 }}}
b : {{{ sqrt(3) }}}
c: {{{ 2 }}}
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This checks out because:
{{{ 1^2 + ( sqrt(3) )^2 = 2^2 }}}
{{{ 1 + 3 = 4 }}}
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Once you put a value on one leg, the 
other legs are known:
given:
{{{ b = 12 }}} ( longer leg )
{{{ a/b = 1/(sqrt(3) ) }}}
{{{ a/12 = 1/(sqrt(3) ) }}}
Multiply both sides by {{{ 12*sqrt(3) }}}
{{{ a*sqrt(3) = 12 }}}
{{{ a = 12/sqrt(3) }}}
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That's the answer. You can check by 
finding c
{{{  a/c = 1/2 }}}
{{{ 1/2 = ( 12/sqrt(3) ) / c }}}
{{{ c = 24/sqrt(3) }}}
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Does {{{ a^2 + b^2 = c^2 }}}?
{{{ ( 12/sqrt(3) )^2 + 12^2 = ( 24/sqrt(3) )^2 }}}
{{{ 144/3 + 144 = 576/3 }}}
{{{ 144 + 3*144 = 576 }}}
{{{ 144 + 432 = 576 }}}
{{{ 576 = 576 }}}
OK