Compound miter brainteaser

Josh · 2006-01-13T16:16:11+00:00

Not for those who don't remember their trigonometry:My father recently built a gazebo. Just for fun, he did it with tensides, rather than the traditional six or eight. He gave the roof a5/12 pitch (22.6 degree angle from horizontal). Thus, the roof wascomprised of 10 triangular wedges. He sheathed the roof with planksforming concentric ten-sided rings around the center.At what angles did he have to miter the planks to get them to fitperfectly?If the roof was flat (zero pitch) like a ten-sided deck, the miterwould have been 36 degrees from perpendicular, with a zero degree tilt(vertical cut). If the roof was infinitely steep (like building thewalls of a ten-sided tower), he would have to have cut the boards witha zero degree miter (perfectly perpendicular cross-cut) with a 36degree tilt from vertical.What would the formula be for N sides with a roof pitch of A degrees?Josh

Jan 13, 2006 43 Replies

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Josh 20 years ago

Nice tutorial.

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alexy 20 years ago

And I guess you can say that anyone that doesn't spot and correct the mixed use of radians and degrees probably shouldn't be trusted with such dangerous formulas!?

Thanks. I'm looking forward to reading that.

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kimnach 20 years ago

i just work in "degrians" until it's time to hit the calculator.

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alexy 20 years ago

LOL! I'll have to remember that one!

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