To measure a dihedral angle, select a
point on the arris
or line of intersection between the planes.
Project lines at right angles from the working point along the surface of each plane of interest.
The dihedral angle is the angle measured between these two lines.
The dihedral angle constructed in the diagrams below is the complement of the Backing Angle.
If the Hip Run = 1, the altitude of of the Hip Triangle is opposite the Hip Pitch Angle
and the run forms the hypotenuse.
Altitude/Run = Altitude/Hypotenuse = Opposite/Hypotenuse = sin Hip Pitch Angle
Opposite/1 = sin Hip Pitch Angle
Opposite = 1 × sin Hip Pitch Angle = Altitude = Backing Angle Rise
If the Hip Run = 1, the Plan Angle Run = 1. With respect to the Plan Angle:
Rise/Run = Rise/1 = Opposite/Adjacent = tan Plan Angle
Opposite/1 = tan Plan Angle
Opposite = 1 × tan Plan Angle = Backing Angle Run
With respect to the Backing Angle:
Backing Angle Rise/Backing Angle Run = Opposite/Adjacent = tan Backing Angle
Backing Angle Rise/Backing Angle Run = Hip Triangle Altitude/Plan Angle Rise
Backing Angle Rise/Backing Angle Run = sin Hip Pitch Angle/tan Plan Angle
tan Backing Angle = sin Hip Pitch Angle/tan Plan Angle
Taking the arctan of both sides of the equation:
Backing Angle = arctan (sin Hip Pitch Angle / tan Plan Angle)