Roof Light Angles

May 2010
Hi I was hoping someone could help me.

I have a old hard copy table that tells me how to work out the pitch of a rafter, the angle under the hip and the dihedral angle.
Pitch = 25° Angle Under Hip = 18.15 Dihedral Angle = 145.25
Pitch = 20° Angle Under Hip = 14.4 Dihedral Angle = 152
Pitch = 40° Angle Under Hip = 30.7 Dihedral Angle = 125.9

Based on this I drew up an end of roof light in 3d. If seems to work. The only angle that it doesn’t give is the cut required on the hip to the rafter connection. From my drawing I can tell the cut needs to be 42°

What I would like to be able to do is add another column to my table that gives me this dimension for each of the different Pitch Scenarios. I could go and draw them all but this one drawing took me ages and I like the saying “work smarter not harder”
I was hoping this is a simple calculation that someone could help me with or point me in the right direction?

i have attached a few pictures to to help clarify. You will notice the 3d drawing shows the angle between the hip and the rafter as 42° when dimensioned but 45° when dimensioned in plan.

Thanks for any help and taking the time to read