SOLUTION: A regular decagon is inscribed in a circle of radius 10m. Find the length of a side of the decagon.

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Question 1131843: A regular decagon is inscribed in a circle of radius 10m. Find the length of a side of the decagon.
Answer by MathLover1(20850) About Me  (Show Source):
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A decagon is a ten sided polygon.
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from right triangle APO we have that apothem a is sqrt%28r%5E2-%28s%2F2%29%5E2%29
and sin%28144%2F2=72%29º
a+=+r+sin%2872%29
a+=+0.951+r+-> since r=10
a+=+9.51056516295153572

then, side s will be
a=sqrt%28r%5E2-%28s%2F2%29%5E2%29
9.51056516295153572=sqrt%2810%5E2-%28s%2F2%29%5E2%29
9.51056516295153572%5E2=100-%28s%2F2%29%5E2
%28s%2F2%29%5E2=100-9.51056516295153572%5E2
%28s%2F2%29%5E2=9.5491502812526288170334064935640816
%28s%2F2%29=sqrt%289.5491502812526288170334064935640816%29
%28s%2F2%29=3.0901699437494742446065683660420445
s=3.0901699437494742446065683660420445%2A2
s=6.180339887498948489213136732084089
s=6.18m