Vector Models of Square Tail Fascia
 Main Pitch = 7/12       Adjacent Pitch = 12/12 Angle in Plan between Eaves = 90°

Terminal Points of Vectors
 Main Eave : ( any x , 0 , 0 ) will suffice; Unit Vector ( 1 , 0 , 0 ) is preferred. The diagrams show ( cos Main Plan Angle , 0 , 0 ). Adjacent Eave : Unit Vector ( cos Plan Angle between Eaves , sin Plan Angle between Eaves , 0 ) The Ridge Line co-ordinates are with respect to Unit Runs on the x-y plane Hip Ridge Line : ( cos Main Plan Angle , sin Main Plan Angle , tan Hip Pitch Angle ) Fascia Ridge Line : ( cos Fascia Plan Angle , sin Fascia Plan Angle , tan Fascia Ridge Pitch Angle )

Vector Product Solution of Saw Blade Bevels
 Main (7/12) Side Fascia Saw Blade Bevel Perpendicular to plane bounded by Hip Rafter Ridge and Fascia Ridge r = Hip Rafter Ridge × Fascia Ridge : ( –1 , .87047 , –.49223 ) Perpendicular to plane bounded by Main Eave and Fascia Ridge m = Main Eave × Fascia Ridge : ( 0 , .43523 , .25389 ) Angle between perpendiculars = Dihedral Angle between defined planes arccos ( r · m ÷ |r| |m| ) = .25388 ÷ .71258 = 69.12792° Saw Blade Bevel = 90° – 69.12792° = 20.87208° Adjacent (12/12) Side Fascia Saw Blade Bevel Perpendicular to plane bounded by Hip Rafter Ridge and Fascia Ridge r = Fascia Ridge × Hip Rafter Ridge : ( –1 , .87047 , –.49223 ) Perpendicular to plane bounded by Adjacent Eave and Fascia Ridge a = Adjacent Eave × Fascia Ridge : ( –.86378 , 0 , –.86378 ) Angle between perpendiculars = Dihedral Angle between defined planes arccos ( r · a ÷ |r| |a| ) = 1.28896 ÷ 1.72756 = 41.74496° Saw Blade Bevel = 90° – 41.74496° = 48.25504°

Trigonometric Solution of Saw Blade Bevels

For any Compound Angle to be cut on a stick rectangular in section:

 Main (7/12) Side Calculations Main Sheathing Angle = 63.25779° Main Fascia Angle on the Stick = 49.18024° Main Fascia Saw Blade Bevel = arctan ( sin 49.18024° ÷ tan 63.25779° ) = 20.87256° The Main Side Fascia matches the Ridge Lines Angle between Ridge Lines = arccos ( cos 49.18024° × cos 63.25779° ) = 72.89392° Adjacent (12/12) Side Calculations Adjacent Sheathing Angle = 39.52120° Adjacent Fascia Angle on the Stick = 67.58488° Adjacent Fascia Saw Blade Bevel = arctan ( sin 67.58488° ÷ tan 39.52120° ) = 48.25487° The Adjacent Side Fascia matches the Ridge Lines Angle between Ridge Lines = arccos ( cos 67.58488° × cos 39.52120° ) = 72.89392°