Hip And Valley Rafters For Octagonal And Other Polygons. Before the table of constants for hips and valleys for octagonal and other polygonal roofs can be formed, it is necessary to determine the tangent values of these polygons, as described in Sec. 30.
Proceeding with the octagon, whose tangent was found to be 4.97" when the run of the common rafter was taken as 12", by the formula c2 = a2+b,i Fig. 72, the run of the octagon hip or valley will be found to be 12.99" for each foot of run of the common rafter.