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| Math Central | Quandaries & Queries |
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Question from Cassie: I'm trying to construct a Wishing Well made of treated 2x4 wood, so the actual measurement is 3 1/2 by 1 1/2. The well is going to be three feet in diameter. I'm trying to construct this as circular as possible, what angle should the wood panels be cut at? |
Suppose the wishing well has n sides. I drew a picture assuming n = 8 and I'll use it to develop a formula for the angle that will work for any n.
Since there are n sides the measure of the angle BCA is 360/n degrees. The measures of the angles CAB and ABC are equal and the sum of the angles of a triangle is always 180 degrees and hence the measure of the angle ABC is
1/2 (180 - 360/n).
This simplifies to
angle ABC = 90 - 180/n degrees.
Thus for example if n = 8 then the measure of the angle ABC is 90 - 180/8 = 90 - 22.5 = 67.5 degrees.
I hope this helps,
Penny
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