If anyone is interested here is how I resolved the compound angles on the purlins. These actually were the solutions of the miter and bevel angles on the faces of square tail fascia perpendicular to the roof of the dormer. (Square fascia, purlins, who cares? Same thing). The method shows the use of ratio and proportion for those who don’t feel comfortable with trig and the angles can of course be solved by development.
This first link is the Purlin/Main Roof Intersection: General Solution ; the intersection of the ridge lines in plan may be any value.
Most ridge lines will intersect at 90° in plan. Here’s a link to an easier solution of the Purlin/Main Roof Intersection: Angle between Ridges equals 90 Degrees .
The cut the compound angle from the face of the purlin set in the plane of the dormer roof the angle on the purlin will follow angle 90° – P2a (i.e., the Main Roof/Dormer intersection follows the Valley trough line). The saw miter will be P2a, the saw blade bevel equals 90° – (C5m + C5a).
The roof ridge lines for these solutions are assumed to lie on a level plane. But many eyebrow dormers have sloping ridge lines ...