Irregular Hip Jack Rafters
Compound Angle Calculations

10/12 Main Jack Rafters
 Jack Rafter Side Cut Angle = 34.92979° 90° – Common Rafter Pitch Angle = 50.19443° Blade Bevel along parallel to Hip Ridge Line = arctan (sin 34.92979° ÷ tan 50.19443°) = 25.50784° = Backing Angle Blade Bevel along Plumb Line = arctan (sin 50.19443° ÷ tan 34.92979°) = 47.72631° = Plan Angle Angle created on Jack Rafter Face meets plumb Face of Hip = arccos (cos 50.19443° × cos 34.92979°) = 58.34132° = Complement of Hip Pitch Angle

11/12 Adjoining Jack Rafters
 Jack Rafter Side Cut Angle = 39.03754° 90° – Common Rafter Pitch Angle = 47.48955° Blade Bevel along parallel to Hip Ridge Line = arctan (sin 39.03754° ÷ tan 47.48955°) = 29.99972° = Backing Angle Blade Bevel along Plumb Line = arctan (sin 47.48955° ÷ tan 39.03754°) = 42.27369° = Plan Angle Angle created on Jack Rafter Face meets plumb Face of Hip = arccos (cos 47.48955° × cos 39.03754°) = 58.34132° = Complement of Hip Pitch Angle

Irregular Valley Jack Rafters
Compound Angle Calculations

12/12 Main Jack Rafters
 Jack Rafter Side Cut Angle = 46.68614° 90° – Common Rafter Pitch Angle = 45.00000° Blade Bevel along parallel to Valley Trough Line = arctan (sin 46.68614° ÷ tan 45.00000°) = 36.03989° = Backing Angle Blade Bevel along Plumb Line = arctan (sin 45.00000° ÷ tan 46.68614°) = 33.69007° = Plan Angle Angle created on Jack Rafter Face meets plumb Face of Valley = arccos (cos 45.00000° × cos 46.68614°) = 60.98286° = Complement of Valley Pitch Angle

8/12 Dormer Jack Rafters
 Jack Rafter Side Cut Angle = 29.01714° 90° – Common Rafter Pitch Angle = 56.30993° Blade Bevel along parallel to Valley Trough Line = arctan (sin 29.01714° ÷ tan 56.30993°) = 17.92021° = Backing Angle Blade Bevel along Plumb Line = arctan (sin 56.30993° ÷ tan 29.01714°) = 56.30993° = Plan Angle Angle created on Jack Rafter Face meets plumb Face of Valley = arccos (cos 56.30993° × cos 29.01714°) = 60.98286° = Complement of Valley Pitch Angle