Question 990884
You want to put a 16-sided regular polygonal {Hexadecagonal) deck
around a 24 foot circular pool.
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The angle between sides,x (interior angle):(n=number of sides=16)
{{{x=((n-2)/n) * 180}}}
{{{x=((16-2)/16)*180}}}
{{{x=(14/16)*180}}}
{{{x=157.5}}} The angle to cut is 1/2 this angle.
ANSWER 1: The angle to cut is 78.75 degrees (both ends).
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For each side tangent to a 24 foot circle:
(each side of the deck will touch the pool at its midpoint)
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a=side length; r=radius=12 feet
.
{{{a=2rtan(180/n)}}}
{{{a=2(12ft)tan(180/16)}}}
{{{a=24ft(0.1989)}}}
{{{a=4.77ft}}}
ANSWER 2:The side length is 4 feet 9 and 1/4 inch.