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
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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° |
