Quote of the Day
The only hope of a pure mathematician is to die before their work is applied.
— Pure mathematician stunned to hear that his work found an application in string theory.
I am considering building a small structure at my lake cabin that has a hip roof. The structure will look a little bit like the one shown in Figure 1 (source), but with a steeper roof pitch.
To build this structure, I need to compute a few angles and, unfortunately, I have forgotten how to determine them using a steel square. To derive formulas for the critical angles, we need to define some terms, which I do in Figure 2. Using these angle definitions, I will derive formulas for the sheathing (θS) and hip pitch angle (θH) given the common pitch angle (which I call the roof pitch [θR]) and plan angle (θP).
Figure 3 shows my derivation. The derivation uses basic geometry, so I will just let the drawing stand for itself. If more detail is needed, send me a note. I will use this post to document formulas as I need them.
I did find formulas for these angles presented on this web page, but no derivation was given − that's no fun at all!