# The area of a right triangle is 32sqrt(3). One of the acute angles is 30^(circ). Find the length of the hypotenuse

The area of a right triangle is $32\sqrt{3}$. One of the acute angles is ${30}^{\circ }$. Find the length of the hypotenuse.
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ignaciopastorp6
a, b --- legs
c --- hypotenuse
c = 2a --- the leg against an angle of 30 degrees is equal to half the hypotenuse
$S=0.5\ast a\ast b=32\sqrt{3}$
$ab=64\sqrt{3}$
${c}^{2}={a}^{2}+{b}^{2}$
$4{a}^{2}={a}^{2}+\left(64\sqrt{3}/a{\right)}^{2}$
$3{a}^{2}={64}^{2}\ast 3/{a}^{2}$
${a}^{4}={64}^{2}$
${a}^{2}=64$
a = 8
c = 16