Using Geometry to Make a Roof

Date: 8/30/95 at 12:18:40
From: Jeff Robertson
Subject: polyhedron

I'm not a student but a wood worker with a question on solid 
geometry. I want to know how to calculate the angle on the sides 
of triangles in order to form a cone shaped (not round but 
angular) roof. I can calculate the base angle required to make 
the roof stand flat but can only use trial and error to get the 
angle that will make the sides come together.

Date: 9/1/95 at 16:8:36
From: Doctor Ken
Subject: Re: polyhedron

Hello!

Probably the best thing to do in this situation would be to find 
a  triangle that contains your angle, and then try to figure out 
everything about the triangle.  For instance, you find a 
triangle that contains the angle in question, then you figure 
out what the lengths of the three sides are, and you use 
trigonometry to figure out the angle you want.  Or you can find 
the correct triangle, and measure the non-base angle of it 
(since it's isosceles).

Can you get it now?  I'd probably use the triangle made of the 
three following points: the center of the base of the cone, and 
the two points where the cone hits the edges of the cone 
perpendicularly.  Then the two base angles of this triangle will 
be the angles you're looking for.

- Doctor Ken,  The Geometry Forum