Advanced Geometry (Cone Segments) Question

Cyryn

New member
Joined
Oct 26, 2016
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This is a real-world problem, so this isn't coming from a text book or anything. Due to that, if I leave out some information I apologize.

I am designing a tent and the top of the tent is a cone. It's also patterned (8 equal segments of the cone complete the pattern). I've included a picture of the paper model for what I'm designing (it's not to scale).

260bf6a.jpg


I now need to figure out the math of the design in order to create a template for cutting out the fabric. The measurements for the cone that I have and know are as follows:

Slope: 117.56"
Height: 73.54"
Diameter: 183.44"
Circumference: 588.32"

I have this image that I'm working on to figure out my math and I'm stuck. I need to find a and b (labeled in image) to start with. I *think* once I find those measurements, I can find the rest of the measurements I need, but I'm completely stumped where to go from here.

143fiti.jpg


In case you can't read my writing, the measurements on the image are as follows:

Slope (left outside edge): 117.56"
Arc Segment (1/8 of circumference): 73.54"
1/2 Slope (right outside edge): 58.78"
 
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