ALPHABETICAL ANGLE FORMULA LIST [A5] [A7] [A8] [A9] [C1] [C2] [C5] [DD] [HC] [P1] [P2] [P3] [P4] [P4BV] [P5] [P5BV] [P6] [Q1] [Q2] [Q3] [Q4] [R1] [R2] [R3] [R4] [R5] [R6B] [R6P] [R6BBV] [R6PBV] [R7] [R7BV] [SS] [VC] [VP] [Misc] [Deck] [Sum] [DD>90] [Base-Peak] [Projected Chamfers] [Square Cut Fascia] [Layover Purlin intersects Main Roof] A5 [INDEX] cosA5 = cosR1 / cosR5 cosA5B = cosDD / cosR4B cosA5B = cosR6B cosR6BBV cosA5B = tanR4B / tanHC cosA5P = cosC5 / cosP6 cosA5P = cosP3 / cosQ4 cosA5P = cosR6P cosR6PBV cosA5P = sinC2 / sinP6 cosA5P = sinDD / cosR4P cosA5P = sinP2 / sinR4P cosA5P = tanR4P / tanVC sinA5 = tanR5 tanR4 sinA5B = sinR1 sinDD sinA5B = sinR6B / sinHC sinA5B = sinR6BBV / cosR4B sinA5P = sinC2 / tanP2 sinA5P = sinC5 cosP2 sinA5P = sinDD tanC5 sinA5P = sinP3 cosC2 sinA5P = sinR1 cosDD sinA5P = sinR6P / sinVC sinA5P = sinR6PBV / cosR4P sinA5P = tanP3 cosC5 sinA5P = tanP6 / tanR4P sinA5P = tanQ4 / tanP6 sinA5P = tanR1 sinP2 tanA5 = sinR4 tanR1 tanA5B = sinR5B tanDD tanA5B = tanR6B / sinR4B tanA5P = cosP6 tanP3 tanA5P = sinP6 / tanP2 tanA5P = sinQ4 / tanC2 tanA5P = sinR5P / tanDD tanA5P = tanC5 cosR4P tanA5P = tanR6P / sinR4P A7 [INDEX] cosA7 = cosC5 cosA9 cosA7 = cosSS / cosP5BV cosA7 = sinP5 / sinDD cosA7 = tanP5BV / tanR1 sinA7 = sinA9 / sinR1 sinA7 = sinC5 / cosP5BV sinA7 = sinSS cosP5 sinA7 = tanP5BV / tanDD tanA7 = sinC5 / cosSS tanA7 = sinP5BV / tanP5 tanA7 = tanC5 / cosR1 tanA7 = tanR1 / tanDD tanA7 = tanSS cosDD A8 [INDEX] cosA8 = cosR2 / cosP4BV cosA8 = sinQ1 / cosC5 sinA8 = sinR2 cosQ1 sinA8 = tanC5 tanP4BV tanA8 = sinC5 tanR2 tanA8 = sinP4BV / tanQ1 A9 [INDEX] cosA9 = cosA7 / cosC5 cosA9 = cosR1 / cosP5BV sinA9 = sinA7 sinR1 sinA9 = tanC5 tanP5BV tanA9 = sinC5 tanR1 C1 [INDEX] cosC1 = 1/ tanP1 tanQ1 cosC1 = cosP2 / cosR2 cosC1 = cosP4 cosP4BV cosC1 = cosR3 / sinQ2 cosC1 = sinC2 / sinR2 cosC1 = sinC5 / sinP1 cosC1 = sinDD / cosP1 cosC1 = sinSS / sinQ3 sinC1 = 1/ tanQ2 tanR2 sinC1 = cosC5 sinP2 sinC1 = cosDD cosSS sinC1 = sinC2 / tanC5 sinC1 = sinC5 / tanSS sinC1 = sinP4 / sinQ1 sinC1 = sinP4BV / sinP1 sinC1 = sinR3 cosC2 sinC1 = tanP1 / tanQ3 sinC1 = tanP2 sinDD sinC1 = tanR2 / tanP1 sinC1 = tanR3 cosP2 tanC1 = cosP1 tanP2 tanC1 = cosQ2 / tanC2 tanC1 = cosQ3 / tanDD tanC1 = cosR2 tanR3 tanC1 = sinP1 / tanSS tanC1 = sinP4BV / sinC5 tanC1 = sinR2 / tanC5 tanC1 = tanP4 / cosP1 tanC1 = tanP4BV / cosQ1 tanC1 = tanQ1 tanR2 C2 [INDEX] cosC2 = 1/ tanR3 tanVP cosC2 = cosC5 / cosP3 cosC2 = cosP2 / cosR3 cosC2 = cosP6 / cosQ4 cosC2 = cosR2 / sinQ2 cosC2 = cosR7 cosR7BV cosC2 = sinA5P / sinP3 cosC2 = sinC1 / sinR3 sinC2 = 1/ tanQ2 tanR3 sinC2 = cosA5P sinP6 sinC2 = sinC1 tanC5 sinC2 = sinC5 sinP2 sinC2 = sinR2 cosC1 sinC2 = sinR7 / sinVP sinC2 = sinR7BV / sinR3 sinC2 = tanP2 sinA5P sinC2 = tanP6 cosC5 sinC2 = tanQ4 / tanP3 sinC2 = tanR2 cosP2 sinC2 = tanR3 tanP3 tanC2 = cosP3 tanP6 tanC2 = cosQ2 / tanC1 tanC2 = cosR3 tanR2 tanC2 = sinP3 tanP2 tanC2 = sinQ4 / tanA5P tanC2 = tanC5 sinR3 tanC2 = tanR7 / cosR3 tanC2 = tanVP / tanQ2 C5 [INDEX] cosC5 = cosA7 / cosA9 cosC5 = cosP1 / cosR2 cosC5 = cosP3 cosC2 cosC5 = cosP6 cosA5P cosC5 = cosSS / cosR1 cosC5 = sinA5P / tanP3 cosC5 = sinC1 / sinP2 cosC5 = sinC2 / tanP6 cosC5 = sinDD / cosP2 cosC5 = sinP4BV / sinR2 cosC5 = sinP5BV / sinR1 cosC5 = sinQ1 / cosA8 cosC5 = tanP2 / tanR4P cosC5 = tanR3 / tanP2 sinC5 = cosP1 / tanQ1 sinC5 = cosQ1 cosP4BV sinC5 = sinA5P / cosP2 sinC5 = sinA7 cosP5BV sinC5 = sinC2 / sinP2 sinC5 = sinP1 cosC1 sinC5 = sinP3 / cosR3 sinC5 = sinP4BV / tanC1 sinC5 = sinP5BV / tanDD sinC5 = sinP6 / sinR4P sinC5 = sinSS cosDD sinC5 = tanA7 cosSS sinC5 = tanA8 / tanR2 sinC5 = tanA9 / tanR1 sinC5 = tanP1 sinDD sinC5 = tanR1 tanP2 sinC5 = tanR2 / tanP2 sinC5 = tanSS sinC1 tanC5 = cosP2 tanP1 tanC5 = cosR2 / tanQ1 tanC5 = sinA5P / sinDD tanC5 = sinA8 / tanP4BV tanC5 = sinA9 / tanP5BV tanC5 = sinC2 / sinC1 tanC5 = sinR1 / tanDD tanC5 = sinR2 / tanC1 tanC5 = tanA5P / cosR4P tanC5 = tanA7 cosR1 tanC5 = tanC2 / sinR3 tanC5 = tanP3 / cosP2 tanC5 = tanP6 / sinP2 tanC5 = tanR2 / tanR3 tanC5 = tanR4P tanR1 tanC5 = tanSS sinP2 DD [INDEX] cosDD = cosP5BV cosP5 cosDD = cosR4B cosA5B cosDD = sinA5P / sinR1 cosDD = sinC1 / cosSS cosDD = sinC5 / sinSS cosDD = sinP1 / sinQ3 cosDD = sinP2 / cosR1 cosDD = sinR4P / cosR5P cosDD = tanA7 / tanSS cosDD = tanR5B / tanR1 sinDD = cosC5 cosP2 sinDD = cosP1 cosC1 sinDD = cosR4P cosA5P sinDD = sinA5B / sinR1 sinDD = sinA5P / tanC5 sinDD = sinC1 / tanP2 sinDD = sinC5 / tanP1 sinDD = sinP2 / tanR4P sinDD = sinP5 / cosA7 sinDD = sinP5BV / sinSS sinDD = sinR4B / cosR5B sinDD = tanR1 / tanSS sinDD = tanR5P / tanR1 sinDD = tanSS / tanQ3 tanDD = cosQ3 / tanC1 tanDD = cosR1 / tanR4P tanDD = cosSS / tanP2 tanDD = sinP5BV / sinC5 tanDD = sinR1 / tanC5 tanDD = sinR5P / tanA5P tanDD = sinSS / tanP1 tanDD = tanA5B / sinR5B tanDD = tanP5 / cosSS tanDD = tanP5BV / sinA7 tanDD = tanR1 / tanA7 tanDD = tanR4B / cosR1 HC [INDEX] cosHC = cosR4B cosR6B sinHC = sinR4B / cosR6BBV sinHC = sinR6B / sinA5B tanHC = tanR4B / cosA5B tanHC = tanR6B / sinR6BBV P1 [INDEX] cosP1 = cosP4BV sinQ1 cosP1 = cosQ3 / cosSS cosP1 = cosR2 cosC5 cosP1 = sinDD / cosC1 cosP1 = sinP4BV / tanR2 cosP1 = tanC1 / tanP2 cosP1 = tanP4 / tanC1 cosP1 = tanQ1 sinC5 sinP1 = cosQ1 / cosP4 sinP1 = sinC5 / cosC1 sinP1 = sinP4BV / sinC1 sinP1 = sinQ3 cosDD sinP1 = sinR2 / sinP2 sinP1 = tanC1 tanSS tanP1 = 1/ cosC1 tanQ1 tanP1 = sinC1 tanQ3 tanP1 = sinC5 / sinDD tanP1 = sinSS / tanDD tanP1 = tanC5 / cosP2 tanP1 = tanP2 tanSS tanP1 = tanP4BV / sinP4 tanP1 = tanR2 / sinC1 P2 [INDEX] cosP2 = cosC1 cosR2 cosP2 = cosC2 cosR3 cosP2 = cosR4P / cosP6 cosP2 = sinA5P / sinC5 cosP2 = sinC1 / tanR3 cosP2 = sinC2 / tanR2 cosP2 = sinDD / cosC5 cosP2 = sinR1 / sinSS cosP2 = tanC5 / tanP1 cosP2 = tanP3 / tanC5 sinP2 = cosA5P sinR4P sinP2 = cosDD cosR1 sinP2 = sinA5P / tanR1 sinP2 = sinC1 / cosC5 sinP2 = sinC2 / sinC5 sinP2 = sinR2 / sinP1 sinP2 = sinR3 / cosP3 sinP2 = tanC5 / tanSS sinP2 = tanP6 / tanC5 sinP2 = tanR4P sinDD tanP2 = cosC5 tanR4P tanP2 = cosSS / tanDD tanP2 = sinC1 / sinDD tanP2 = sinC2 / sinA5P tanP2 = sinC5 / tanR1 tanP2 = sinP6 / tanA5P tanP2 = tanC1 / cosP1 tanP2 = tanC2 / sinP3 tanP2 = tanP1 / tanSS tanP2 = tanP6 / tanP3 tanP2 = tanR2 / sinC5 tanP2 = tanR3 / cosC5 P3 [INDEX] cosP3 = cosA5P cosQ4 cosP3 = cosC5 / cosC2 cosP3 = sinR3 / sinP2 cosP3 = tanC2 / tanP6 sinP3 = sinA5P / cosC2 sinP3 = sinC5 cosR3 sinP3 = sinQ4 / sinP6 sinP3 = tanC2 / tanP2 tanP3 = sinA5P / cosC5 tanP3 = sinC2 / tanR3 tanP3 = tanA5P / cosP6 tanP3 = tanC5 cosP2 tanP3 = tanP6 / tanP2 tanP3 = tanQ4 / sinC2 P4 [INDEX] cosP4 = cosC1 / cosP4BV cosP4 = cosQ1 / sinP1 sinP4 = sinC1 sinQ1 sinP4 = tanP4BV / tanP1 tanP4 = tanC1 cosP1 tanP4 = tanQ1 sinP4BV P4BV [INDEX] cosP4BV = cosC1 / cosP4 cosP4BV = cosP1 / sinQ1 cosP4BV = cosR2 / cosA8 cosP4BV = sinC5 / cosQ1 sinP4BV = cosC5 sinR2 sinP4BV = sinC1 sinP1 sinP4BV = tanA8 tanQ1 sinP4BV = tanC1 sinC5 sinP4BV = tanP4 / tanQ1 sinP4BV = tanR2 cosP1 tanP4BV = sinA8 / tanC5 tanP4BV = sinP4 tanP1 tanP4BV = sinQ1 tanR2 tanP4BV = tanC1 cosQ1 P5 [INDEX] cosP5 = cosDD / cosP5BV cosP5 = sinA7 / sinSS sinP5 = cosA7 sinDD sinP5 = tanP5BV / tanSS tanP5 = cosSS tanDD tanP5 = sinP5BV / tanA7 P5BV [INDEX] cosP5BV = cosDD / cosP5 cosP5BV = cosR1 / cosA9 cosP5BV = cosSS / cosA7 cosP5BV = sinC5 / sinA7 sinP5BV = cosC5 sinR1 sinP5BV = sinSS sinDD sinP5BV = tanA7 tanP5 sinP5BV = tanDD sinC5 sinP5BV = tanR1 cosSS tanP5BV = cosA7 tanR1 tanP5BV = sinA7 tanDD tanP5BV = sinA9 / tanC5 tanP5BV = sinP5 tanSS P6 [INDEX] cosP6 = cosC2 cosQ4 cosP6 = cosC5 / cosA5P cosP6 = cosR4P / cosP2 cosP6 = tanA5P / tanP3 sinP6 = sinC2 / cosA5P sinP6 = sinC5 sinR4P sinP6 = sinQ4 / sinP3 sinP6 = tanP2 tanA5P tanP6 = sinC2 / cosC5 tanP6 = tanC2 / cosP3 tanP6 = tanC5 sinP2 tanP6 = tanP2 tanP3 tanP6 = tanQ4 / sinA5P tanP6 = tanR4P sinA5P Q1 [INDEX] cosQ1 = sinA8 / sinR2 cosQ1 = sinC5 / cosP4BV cosQ1 = sinP1 cosP4 cosQ1 = tanP4BV / tanC1 sinQ1 = cosC5 cosA8 sinQ1 = cosP1 / cosP4BV sinQ1 = sinP4 / sinC1 sinQ1 = tanP4BV / tanR2 tanQ1 = 1/ cosC1 tanP1 tanQ1 = cosP1 / sinC5 tanQ1 = cosR2 / tanC5 tanQ1 = sinP4BV / tanA8 tanQ1 = tanC1 / tanR2 tanQ1 = tanP4 / sinP4BV Q2 [INDEX] cosQ2 = sinR2 sinR3 cosQ2 = tanC1 tanC2 sinQ2 = cosR2 / cosC2 sinQ2 = cosR3 / cosC1 tanQ2 = 1/ tanR2 sinC1 tanQ2 = 1/ tanR3 sinC2 tanQ2 = tanVP / tanC2 Q3 [INDEX] cosQ3 = cosSS cosP1 cosQ3 = tanDD tanC1 sinQ3 = sinP1 / cosDD sinQ3 = sinSS / cosC1 tanQ3 = tanP1 / sinC1 tanQ3 = tanSS / sinDD Q4 [INDEX] cosQ4 = cosP3 / cosA5P cosQ4 = cosP6 / cosC2 sinQ4 = sinP3 sinP6 sinQ4 = tanC2 tanA5P tanQ4 = tanP3 sinC2 tanQ4 = tanP6 sinA5P R1 [INDEX] cosR1 = cosA5 cosR5 cosR1 = cosP5BV cosA9 cosR1 = cosSS / cosC5 cosR1 = sinP2 / cosDD cosR1 = tanC5 / tanA7 cosR1 = tanR4B / tanDD cosR1 = tanR4P tanDD sinR1 = sinA5B / sinDD sinR1 = sinA5P / cosDD sinR1 = sinA9 / sinA7 sinR1 = sinP5BV / cosC5 sinR1 = sinR5 / cosR4 sinR1 = sinSS cosP2 sinR1 = tanDD tanC5 tanR1 = sinA5P / sinP2 tanR1 = sinC5 / tanP2 tanR1 = sinP5BV / cosSS tanR1 = tanA5 / sinR4 tanR1 = tanA9 / sinC5 tanR1 = tanC5 / tanR4P tanR1 = tanDD tanA7 tanR1 = tanP5BV / cosA7 tanR1 = tanR5B / cosDD tanR1 = tanR5P / sinDD tanR1 = tanSS sinDD R2 [INDEX] cosR2 = cosP1 / cosC5 cosR2 = cosP2 / cosC1 cosR2 = cosP4BV cosA8 cosR2 = sinQ2 cosC2 cosR2 = tanC1 / tanR3 cosR2 = tanQ1 tanC5 sinR2 = cosQ2 / sinR3 sinR2 = sinA8 / cosQ1 sinR2 = sinC2 / cosC1 sinR2 = sinP2 sinP1 sinR2 = sinP4BV / cosC5 sinR2 = tanC1 tanC5 tanR2 = 1/ tanQ2 sinC1 tanR2 = sinC2 / cosP2 tanR2 = sinC5 tanP2 tanR2 = sinP4BV / cosP1 tanR2 = tanA8 / sinC5 tanR2 = tanC1 / tanQ1 tanR2 = tanC2 / cosR3 tanR2 = tanC5 tanR3 tanR2 = tanP1 sinC1 tanR2 = tanP4BV / sinQ1 R3 [INDEX] cosR3 = cosP2 / cosC2 cosR3 = cosR7BV sinVP cosR3 = sinP3 / sinC5 cosR3 = sinQ2 cosC1 cosR3 = tanC2 / tanR2 cosR3 = tanR7 / tanC2 sinR3 = cosQ2 / sinR2 sinR3 = cosVP / cosR7 sinR3 = sinC1 / cosC2 sinR3 = sinP2 cosP3 sinR3 = sinR7BV / sinC2 sinR3 = tanC2 / tanC5 tanR3 = 1/ cosC2 tanVP tanR3 = 1/ tanQ2 sinC2 tanR3 = cosC5 tanP2 tanR3 = sinC1 / cosP2 tanR3 = sinC2 / tanP3 tanR3 = tanC1 / cosR2 tanR3 = tanR2 / tanC5 tanR3 = tanR7BV / sinR7 R4 [INDEX] cosR4 = sinR5 / sinR1 cosR4B = cosDD / cosA5B cosR4B = cosHC / cosR6B cosR4B = sinR6BBV / sinA5B cosR4P = cosP2 cosP6 cosR4P = cosVC / cosR6P cosR4P = sinDD / cosA5P cosR4P = sinR6PBV / sinA5P cosR4P = tanA5P / tanC5 sinR4 = tanA5 / tanR1 sinR4B = sinDD cosR5B sinR4B = tanR6B / tanA5B sinR4B = cosR6BBV sinHC sinR4P = cosDD cosR5P sinR4P = cosR6PBV sinVC sinR4P = sinP2 / cosA5P sinR4P = sinP6 / sinC5 sinR4P = tanR6P / tanA5P tanR4 = sinA5 / tanR5 tanR4B = cosA5B tanHC tanR4B = cosR1 tanDD tanR4B = cosC5 / (tanP2 + tanA9) * Note value of denominator tanR4B = sinR6B / tanR6BBV tanR4P = cosA5P tanVC tanR4P = cosR1 / tanDD tanR4P = sinP2 / sinDD tanR4P = sinR6P / tanR6PBV tanR4P = tanC5 / tanR1 tanR4P = tanP2 / cosC5 * Note value of numerator tanR4P = tanP6 / sinA5P R5 [INDEX] cosR5 = cosR1 / cosA5 cosR5B = sinR4B / sinDD cosR5P = sinR4P / cosDD sinR5 = sinR1 cosR4 sinR5B = tanA5B / tanDD sinR5P = tanA5P tanDD tanR5 = sinA5 / tanR4 tanR5B = cosDD tanR1 tanR5P = sinDD tanR1 R6B [INDEX] cosR6B = cosA5B / cosR6BBV cosR6B = cosHC / cosR4B sinR6B = sinHC sinA5B sinR6B = tanR4B tanR6BBV tanR6B = tanA5B sinR4B tanR6B = tanHC sinR6BBV R6P [INDEX] cosR6P = cosA5P / cosR6PBV cosR6P = cosVC / cosR4P sinR6P = sinVC sinA5P sinR6P = tanR4P tanR6PBV tanR6P = tanA5P sinR4P tanR6P = tanVC sinR6PBV R6BBV [INDEX] cosR6BBV = cosA5B / cosR6B cosR6BBV = sinR4B / sinHC sinR6BBV = sinA5B cosR4B sinR6BBV = tanR6B / tanHC tanR6BBV = sinR6B / tanR4B R6PBV [INDEX] cosR6PBV = cosA5P / cosR6P cosR6PBV = sinR4P / sinVC sinR6PBV = sinA5P cosR4P sinR6PBV = tanR6P / tanVC tanR6PBV = sinR6P / tanR4P R7 [INDEX] cosR7 = cosC2 / cosR7BV cosR7 = cosVP / sinR3 sinR7 = sinVP sinC2 sinR7 = tanR7BV / tanR3 tanR7 = sinR7BV tanVP tanR7 = tanC2 cosR3 R7BV [INDEX] cosR7BV = cosC2 / cosR7 cosR7BV = cosR3 / sinVP sinR7BV = sinC2 sinR3 sinR7BV = tanR7 / tanVP tanR7BV = sinR7 tanR3 SS [INDEX] cosSS = cosC5 cosR1 cosSS = cosP5BV cosA7 cosSS = cosQ3 / cosP1 cosSS = sinC1 / cosDD cosSS = sinC5 / tanA7 cosSS = sinP5BV / tanR1 cosSS = tanDD tanP2 cosSS = tanP5 / tanDD sinSS = cosC1 sinQ3 sinSS = sinA7 / cosP5 sinSS = sinC5 / cosDD sinSS = sinP5BV / sinDD sinSS = sinR1 / cosP2 sinSS = tanP1 tanDD tanSS = sinC5 / sinC1 tanSS = sinDD tanQ3 tanSS = sinP1 / tanC1 tanSS = tanA7 / cosDD tanSS = tanC5 / sinP2 tanSS = tanP1 / tanP2 tanSS = tanP5BV / sinP5 tanSS = tanR1 / sinDD VC [INDEX] cosVC = cosR4P cosR6P sinVC = sinR4P / cosR6PBV sinVC = sinR6P / sinA5P tanVC = tanR4P / cosA5P tanVC = tanR6P / sinR6PBV VP [INDEX] cosVP = sinR3 cosR7 sinVP = cosR3 / cosR7BV sinVP = sinR7 / sinC2 tanVP = 1/ cosC2 tanR3 tanVP = tanC2 tanQ2 tanVP = tanR7 / sinR7BV MISCELLANEOUS FORMULAS : [INDEX] (Single version of each formula, no transpositions are listed) Deck Angle Formulas: [INDEX] W = DD + D tanDD = sinW / [(tanSS/tanS)+cosW] tanD = sinW / [(tanS/tanSS)+cosW] Sum Formulas: [INDEX] A8 = P2 - P4 A9 = 90° - (P2 + P5) CV = R4P P3 = P1 - (90° - Q2) P6 = SS - R5P PV = 90° - R3 Q2 = P3 + (90° - P1) Q3 = R1 + R2 Q4 = R4P - R3 Projected Chamfer Cut Relations: [INDEX] P3 = P1 - arctan(tanR2 sinC1) P4 = P2 - arctan(tanR2 sinC5) P5 = (90° - P2) - arctan(tanR1 sinC5) P6 = SS - arctan(tanR1 sin DD) R4B = (90° - R4P) - arctan(tanR5P sinA5P) R6B = R1 - arctan(tanR5B cosDD) R6P = R1 - arctan(tanR5P sinDD) R7 = R2 - arctan(sinC1 / tanQ2) If DD or D > 90 Degrees: [INDEX] cos(90° ± C5) = sinSS cosDD cosR1 = cosSS / sin(90° ± C5) cosP2B = cosDD cosR1 cos(90° ± A5B) = sinR1 sinDD cosR5B = cosR1 / sin(90° ± A5B) cosR4B = cosDD / sin(90° ± A5B) Base - Peak (Eave - Ridge) Relationships: [INDEX] sinA5B = sinA5P tanDD sinR5B = sinA5P / cosA5B sinR5P = sinA5B / cosA5P tanR5B = sinA5P / cosR1 tanR5B = tanA5P / cosR5P tanR5P = sinA5B / cosR1 tanR5P = tanA5B / cosR5B tanR5P = tanR5B tanDD cos(R4B + R4P) = sinR5B sinR5P sin(R4B + R4P) = cosR5B / cosA5P sin(R4B + R4P) = cosR5P / cosA5B tan(R4B + R4P) = 1 / (tanR5P sinA5P) tan(R4B + R4P) = 1 / (tanR5B sinA5B) cosR5B / cosA5P = cosR5P / cosA5B Square Cut Fascia Formulas: [INDEX] tanSFMm = sinSS / tanD tanSFMa = sinS / tanDD sinSFBm = cosS cosDD tanSFBm = cosSFMm tanP2m sinSFBa = cosSS cosD tanSFBa = cosSFMa tanP2a cosSFCm = sinSFMm sinP2m cosSFCa = sinSFMa sinP2a cosSFCm = cosSFCa Layover Purlin intersects Main Roof Equations: [INDEX] Main Ridge and Dormer Ridge intercept in Plan = 90° Main Roof Pitch Angle = SS Dormer (Adjacent) Roof Pitch Angle = S Face perpendicular to Dormer Roof sin Saw Blade Bevel sinPLBa = cosSS × sinS tan Saw Blade Miter tanPLMa = cosS / tanSS tan Angle on the Stick tan(90° – PLMa) = tanSS / cosS Face set in Dormer Roof sin Saw Blade Bevel = cosSS × cosS Saw Blade Bevel = 90° – (C5m + C5a) tan Saw Blade Miter = sinS / tanSS Saw Blade Miter = P2a tan Angle on the Stick = tanSS / sinS Angle on the Stick = 90° – P2a tan Angle on Face adjoining Main Roof Slope tanPLCa = tanSS / (cosSS × sinS × cosS) General Case: Main Ridge and Dormer Ridge intercept in Plan = any W Face perpendicular to Dormer Roof tan Saw Blade Bevel tanPLBa = cosPLMa × tanP2a tan Saw Blade Miter tanPLMa = (cosS / tanSS – sinS cosW)/sinW tan Angle on the Stick tan(90° – PLMa) = sinW/(cosS / tanSS – sinS cosW) cos Angle on Face adjoining Main Roof Slope cosPLCa = sinPLMa × sinP2a [INDEX] Joe Bartok 2004 Revised March 2007