8 sided pyramid math problem

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78
Location
Maplewood, NJ
It's too much for my meager math skills.

I'm trying to build a birdfeeder for my wife for Christmas that replicates the gazebo-shaped addition off the back of our house.

The addition has an eight-sided roof that comes to a point in the center, kind of like a squat steeple.

I can calculate the pitch of the roof easily enough, but it's going to be made out of eight pie-wedge shaped pieces of 1/2" ply, and the sides (interior edges) of those pieces need to be beveled to fit tightly. I don't have a clue as to how to calculate the angle of that bevel.

A friend sent me a solution that might be perfect, except I don't understand trigonometry, so I have no idea what he's talking about.

Something tells me there's an easy way to do this. I would bet that millions of such shapes have been created by craftsmen with no knowledge of trig whatsoever.

Here's the basics: The roof of the feeder will be 14" across at the base. It will be 3.5 inches high at the center. At what angle do I need to bevel the pieces so they'll fit together at that pitch?

Thanks!
 
That's some spiffy math you got there Glenn:thumb:
If it was me I would just set the table saw blade at some random angle and rip out some test pieces. If they worked great if they didn't I would adjust according. :thumb:
Way less stressful than doing all that math just to find out that the angle it came up with is wrong and you need to adjust the angle just a bit anyways.:rofl::rofl:
 
I did it graphically in SketchUp in a minute or so. It says that the tablesaw blade needs to be tilted over at 9.854°. If you want the illustrations, I can post them.
 
Yeah, but you were using your fingers and toes. :rofl:

Nope no math just dead reckoning.:thumb:
To be honest I prolly would have put a 5 or 6 on the first time. When that didn't pan most likely would have jumped to 10. Than had to back it off just a smidgen to make your 9.854 on the third try.
Just like field artillery Shoot one low. shoot one high. Than shoot one right down the middle:thumb::rofl::rofl:
 
That's prolly the best way, too.

Here's what I got.

5265080534_1299518c12.jpg

5265080392_6b9833352a.jpg
 
Yeah... well... everybody's right.

I keep trying to remind myself it's not rocket surgery, but I keep falling into the same trap every time anyway. Always want it to be exactly right, it never is, nobody notices (except me). Then next time, it's lather, rinse, repeat.

Think I can take it from here. I bought plenty of 1/2" ply.

Thanks for all the help... especially the pictures. Not sure I understand them, but they look extremely cool. And I understood the 9.854 part, which is the most important one.

Now all I can think of is the ad I saw in the local pennysaver once: "For Sale: Squirrel feeder... doesn't even pretend to be a bird feeder."
 
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