Tréteaux Angles Trigonometry Formulas 

Tréteaux Angles Trigonometry Formulas
Link to Online Script to check the Tréteaux Angles
Input Variables
Works for any Roof Eave Angle with equal or unequal rafter slope angles.
Roof Eave Angle
SS = Main Rafter Slope Angle
S = Adjacent Rafter Slope Angle

DD = Main Plan Angle
D = Adjacent Plan Angle

R1 = Hip Rafter Slope Angle
C5m Main Hip Rafter Backing Angle
C5a Adjacent Hip Rafter Backing Angle
Valley Sleeper Saw Blade Bevel Angle = 90° - (C5m + C5a)

P2m = Main Jack Rafter Side Cut Angle
90° - P2m = Main Roof Sheathing Angle
P2a = Adjacent Jack Rafter Side Cut Angle
90° - P2a = Adjacent Roof Sheathing Angle

Tréteaux Angles
tréteau à devers

R8-DP = Tilted Hip Rafter Slope Angle on DP Side = arctan( tan ( Hip Rafter Backing Angle) ÷ tan (Jack Rafter Side Cut Angle ))
R8-DP = arctan( tan ( C5m )  ÷  tan ( P2m ))

R9-DP = Horizontal Plane Rotation for Tilted Hip Rafter on DP Line
R9-DP = arctan( sin ( R1 ) × tan ( C5m ))

D-DP = Horizontal Plane Rotation for Tilted Hip Rafter on DP Line from Eave Line
D-DP = D - R9

R10-DP = Vertical Plane Rotation for Tilted Hip Rafter on DP Line
R10-DP = arctan((cos(R1) × tan(R9)) / sin(R1));

PSB-DP = Prism Saw Blade Bevel Angle Along side of Hip Rafter Rotated into the Roof Surface Plane
PSB-DP = arctan( sin(90° - P2m) ÷ tan(R8))

SR4Bm-DP = Prism Footprint Angle Along side of Hip Rafter Rotated into the Roof Surface Plane
SR4Bm-DP = arccos( cos(90° - P2m) × cos(R8))

SR4Ba-DP = Prism Footprint Angle Along side of Hip Rafter on Main Plan Angle
SR4Ba-DP = arccos( cos(90° + P2m) × cos(R8))

R11m-DP = Hip Rafter Miter Angle on Side Of Hip Rafter at Peak
R11m-DP = arctan( (sin (90° - P2m ) ÷ tan ( C8 )) ÷ cos (90° - P2m ))

P7m-DP = Purlin Rafter Bevel Angle on Side Face Parallel To Roof Surface
P7m-DP = 90° + P2m
P7m-DP = 90° + 19.01633 = 109.01633
P8m-DP = Purlin Rafter Miter Angle On Top Edge Face Perpendicular to Roof Surface = 90.00°
P9m-DP = Purlin Rafter Saw Blade Bevel Angle Along Miter Angle on Side Face = 0.00°

P10m-DP = Jack Rafter Miter Angle on Side Face Perpendicular to Roof Surface at Hip Rafter Rotated Into Roof Surface
P10m-DP = 90°
P11m-DP = Jack Rafter Bevel Angle On Top Edge Face Set in Roof Surface = P2m  
P12m-DP = Jack Rafter Saw Blade Bevel Angle Along Miter Angle on Side Face = P2m 
P13a-DP = Purlin Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Lower Claw Angle
P13a-DP = arctan( sin (90° - P2a ) ÷ tan ( Valley Sleeper Saw Blade Bevel Angle )) 

P14a-DP = Purlin Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Upper Claw Angle
P14a-DP = arctan( cos ( P2a ) ÷ tan ( 90° -  Valley Sleeper Saw Blade Bevel Angle )) 

P15a-DP = Purlin Rafter Bevel Angle on DP Side Of Hip Rafter on Face Set in Roof Surface
P15a-DP = 90° - P2a

P16a-DP = Jack Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Lower Claw Angle
P16a-DP = arctan( sin ( P2a ) × tan (90° - Valley Sleeper Saw Blade Bevel Angle )) 

P17a-DP = Jack Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Upper Claw Angle
P17a-DP = arctan( sin ( P2a ) × tan ( Valley Sleeper Saw Blade Bevel Angle )) 

P18a-DP = Jack Rafter Bevel Angle on DP Side Of Hip Rafter on Face Set in Roof Surface
P18a-DP = P2a
Control files for Roof Eave Angle = 90° , 7:12 & 10:12 roof pitch






Control files for Roof Eave Angle = 120° , 7:12 & 10:12 roof pitch





































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