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| Math Central | Quandaries & Queries |
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Question from Kenneth: I am 35 yr I am wanting to build a well house cover. I'm trying to figure out how long the pieces need to be and what angle they need to be for a 4 ft dia with 14 side well house. I would love an answer but would also like to know how to figure it in the future. Thanks Kd |
Kenneth,
Join each pair of opposite vertices to form 14 congruent triangles. One such triangle is ABC below.
The angle BCA has measure 360/14 = 25.71 degrees.
I redrew triangle ABC and let D be the midpoint of AB so
the measure of angle BCD = 25.71/2 = 12.86 degrees.
You said a 4 foot diameter so |CD| = 2 feet = 24 inches. Thus tan(12.86) = |DB|/|CD| and thus
|DB| = |CD| tan(12.86) = 24 × 0.2282 = 5.48 inches.
Thus
|AB| = 2 × 5.48 = 10.96 inches which is 10 15/16 inches.
I hope this helps,
Harley
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