Regular Roof Slope Angle

Unit Rise
Slope Angle atan(unitrise / 12 )
Hip Slope Angle atan(unitrise)/sqrt(288)
Backing Angle atan(sin(hip slope angle))



Angles for an Irregular Roof

Major Roof Pitch
Minor Roof Pitch
Major Plan Angle
atan(minor/major)

angle in plan on the steeper side.
working with the example of the 8/12, 10/12
8/10 =.8 , arc tan .8= 38.659 degrees
= plan angle of 10/12 side
Minor Plan Angle
atan(major/minor)

angle in plan of the shallower-pitched roof.
51.34 degrees = plan angle of 8/12 side
Hip Run per Foot 8x10 divide 12= 6.666 =rise
8 divide 10 =.8 , arc tan .8 =38.65 degrees
cos 1x 38.659 = 1.2806
1.2806 x 10 =12.806 = hip run for 8-10 runs
Angle of Hip 6.666 divide 12.806 =.5205
arc tan .5205 =27.498 degrees
= angle of hip
Backing Angle Shallow Side of Hip sine 27.498 = .4617= rise of backing angles
tan 51.34 degrees = 1.2499
.4617 divide 1.2499 = .369
arc tan .369 =20.27 degrees
= saw backing bevel for 8/12 side of hip
Backing Angle Steep side of Hip tan 38.659 = .799 , .4617 divide .799= .577
arc tan .577 =29.99 degrees
= saw backing bevel of 10/12 side of hip.