SOLUTION: Find the length, to the nearest tenth, of the apothem of a regular octagon whose sides are 10 inches long?????
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-> SOLUTION: Find the length, to the nearest tenth, of the apothem of a regular octagon whose sides are 10 inches long?????
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Question 145658: Find the length, to the nearest tenth, of the apothem of a regular octagon whose sides are 10 inches long????? Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! For a detailed explanation of apothem and octagon see:
http://www.mathsisfun.com/geometry/regular-polygons.html
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Use radians NOT degrees...
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Side = 2 × Radius × sin(π/n)
where
n = number of sides
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Stuff in the information from the problem:
10 = 2 × Radius × sin(π/8)
5 = Radius × sin(π/8)
5/sin(π/8) = Radius
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Then, because
Apothem = Radius × cos(π/n)
Apothem = 5/sin(π/8) × cos(π/8)
Apothem = 5cos(π/8)/sin(π/8)
Apothem = 5cos(π/8)/sin(π/8)
