Square Cut Fascia on Dormer
intercepts Plane of Main Roof

Trigonometric Solutions using the
Main Roof Pitch Angle and Dormer Pitch Angle

Main Roof Ridge and Dormer Ridge intercept is assumed to be 90°
Online Calculator: Square Fascia meets Main Roof
Hip Roof Model of Square Fascia meets Main Roof
 The geometry of the model is identical to the geometry of a Hip Roof. The angle labelled Hip Pitch Angle in the diagram actually lies on the plane of the 7/12 Main Roof. Solution of the Saw Blade Bevel The Dormer Pitch Angle of 39.80557° occupies the same position on the model as the Common Rafter Pitch Angle on a Hip Roof. The Main Roof Pitch Angle of 30.25644° occupies the same position on the model as the Plan Angle on a Hip Roof. The Saw Blade Bevel Angle occupies the same position on the model as the Backing Angle on a Hip Roof. The solution given in the drawing substitutes the model ratios for the trig functions of the angles in the well-known formula: Backing Angle = arctan (sin Hip Pitch Angle ÷ tan Plan Angle) But the Backing Angle for a Hip Rafter may also be calculated directly from the Common Rafter Pitch Angle and Plan Angle by: Backing Angle = arcsin (sin Common Rafter Pitch Angle × cos Plan Angle) Noting the positions of the angles on the model we make the following substitutions: Saw Blade Bevel Angle = arcsin (sin Dormer Pitch Angle × cos Main Roof Pitch Angle) = arcsin (sin 39.80557° × cos 30.25644°) = 33.57154° Solution of the Saw Miter Angle and Angle on the Fascia The Dormer Pitch Angle of 39.80557° occupies the same position on the model as the Common Rafter Pitch Angle on a Hip Roof. The Main Roof Pitch Angle of 30.25644° occupies the same position on the model as the Plan Angle on a Hip Roof. The Saw Miter Angle occupies the same position on the model as the Jack Rafter Side Cut Angle on a Hip Roof. Jack Rafter Side Cut Angle = arctan (cos Common Rafter Pitch Angle ÷ tan Plan Angle) Noting the positions of the angles on the model we make the following substitutions: Saw Miter Angle = arctan (cos Dormer Pitch Angle ÷ tan Main Roof Pitch Angle) = arctan (cos 39.80557° ÷ tan 30.25644°) = 52.78951° The complementary Angle on the Fascia is located in the same position on the model as the Sheathing Angle on a Hip Roof. Sheathing Angle = arctan (tan Plan Angle ÷ cos Common Rafter Pitch Angle) Noting the positions of the angles on the model we make the following substitutions: Angle on the Fascia = arctan (tan Main Roof Pitch Angle ÷ cos Dormer Pitch Angle) = arctan (tan 30.25644° ÷ cos 39.80557°) = 37.21049°