Backing Angle ... the animated version. The right angle at the corner can actually be any value.
Construction of the Backing Angle Backing Angle: Regular Octogonal Gazebo Setting the length of the Hip run equal to one, the length of the line perpendicular to the Hip rafter and forming the rise of the backing angle is sin
Hip Pitch Angle. The line of the backing angle run in plan view equals tan
Plan Angle.
Since the rise/run of an angle is the tangent we can derive the well known formula (one of many ...) for the backing bevel:
tan
Backing Angle = sin
Hip Pitch Angle ÷ tan
Plan AngleTaking the arctangent of both sides of the equation:
Backing Angle = arctan (sin
Hip Pitch Angle ÷ tan
Plan Angle)