Scott, a student in our Ancient Knowledge Tour class on roof framing geometry, asked where you would use the unequal pitched roof framing geometry on a job site. This would be an easy example of using geometry on the jobsite.
The main roof pitch was 4:12 and the roof dormer pitch was a 6:12 pitch. So I draw out an L on the drawing board and marked off 4" & 6" on each side of the L. Then I drew perpendicular lines from those marks. From the intersection of the perpendicular lines I drew in the hip-valley run line. Next I drew in the hip rafter basic shift to establish the location of the sides of the hip-valley in plan view. I placed the jack rafter tail at 9" from the intersection of the two roof pitches. With the jack rafter tail in plan view I picked up the exact length of the jack rafter tail on the horizontal plane placed at 9" from the intersection of the two roof pitches. I also able to draw out the jack rafter tail plumb line shift to layout the cut on the jack rafter tail.
Then I drew the hip-valley rafter in profile to determined the length of the valley rafter tail. As well as the valley rafter tail plumb line shift for the cut at the peak of the valley rafter tail and the "V" notch at the foot of the valley rafter tail.
Here are some drawings with the different steps to draw out the geometry for the unequal pitched valley rafter tail.