There are a wealth of roofing calculators on the interweb, e.g...

https://www.blocklayer.com/roof/roofeng.aspx

I don't know if they will be of help to your specific problem but they may be useful in checking the solution at which you arrive.

In my experience, solid geometry problems have always been easier to solve if expressed in vector form and then attacked with analytic geometry.

At any rate, good luck with your work.