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

Joe Bartok

[INDEX]

Joe Bartok 2004

Revised March 2007

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