Question 1072904
If by "height" is meant "altitude", then this being in the plane of the deck. cuts this equilateral triangle shape into two congruent  special 30-60-90 right triangles.  


Do you see?  Pythagorean Theorem, and hypotenuse is the length of one side of the deck.



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Half the equilateral triangle, special 30-60-90

leg, 27 feet
leg, x
hypotenuse, 2x
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{{{x^2+27^2=(2x)^2}}}
{{{x^2+27^2=4x^2}}}
{{{27^2=3x^2}}}
{{{3x^2=3*9*27}}}
{{{x^2=9*27}}}
{{{x^2=9*9*3}}}
{{{x=9sqrt(3)}}}
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side of the equilateral triangle, {{{2x=highlight(18*sqrt(3))}}}