1. Dormer Shed Roof Rafter Length
2. Dormer Shed Roof Miter Angle (Rake Cut Angle)
3. Dormer Shed Roof Sleeper Bevel Length
4. Dormer Shed Roof Intercept Run ( Intersection of Dormer Roof and Main Roof)
5. Main Roof Intercept Length (Useful for laying out Dormer Sleeper that is not Beveled)

Using the Law of Sines 
c = ( a * sin( C ) ) ÷ sin( A)

c = Dormer Roof Rafter Length
C1 = 90° - Dormer Roof Pitch Angle
C2 = 90° - (Main Roof Pitch Angle - Dormer Roof Pitch Angle)
C = 90° - Dormer Roof Pitch Angle + (90° - (Main Roof Pitch Angle - Dormer Roof Pitch Angle))
C = C1 + C2
A = Main Roof Pitch Angle - Dormer Roof Pitch Angle  
a = Dormer Roof Run

Dormer Roof Rafter Length = (Dormer Roof Run * sin(90° - Dormer Roof Pitch Angle + (90° - (Main Roof Pitch Angle - Dormer Roof Pitch Angle)))) ÷ sin(Main Roof Pitch Angle - Dormer Roof Pitch Angle )
or
Dormer Roof Rafter Length = (Dormer Roof Run * sin(C)) ÷ sin(A)
or
 
Dormer Altitude = sin(Dormer Roof Pitch Angle) *  Dormer Run
Dormer Altitude Run = Dormer Altitude ÷ tan(Dormer Roof Pitch Angle)
Dormer Miter Cut Angle =  Main Roof Pitch Angle - Dormer Roof  Pitch Angle
Main Altitude Run = Dormer Altitude ÷ tan(Dormer Miter Cut Angle)
Dormer Rafter Length = Dormer Altitude Run + Main Altitude Run
Main Intercept Run = (Dormer Rafter Length  * cos( Dormer Roof Pitch Angle)) - Dormer Run

An example of the calculated results that you can email yourself in the Rafter Tools app 

•  Main Rafter Slope Angle
•  33.69007°
•  Main Rafter Pitch
•  8  in\12in
•  Main Rafter HAP
•  7 3/4''in
•  Main Roof Sheathing Material Thickness
•  1/2''in
•  Main Roof Rafter Material Depth
•  9 1/2''in
•  Main Roof Rafter Plumb Height
•  11 7/16''in
•  Main Run
•  28 1/4''in
•  Main Intercept Run
•  32 7/16''in
•  Dormer Rafter Slope Angle
•  14.03624°
•  Dormer Rafter Pitch
•  3  in\12in
•  Dormer Rafter HAP
•  8 7/16''in
•  Dormer Run
•  54 ''in
•  Dormer Roof Rafter Material Depth
•  9 1/2''in
•  Dormer Roof Rafter Plumb Height
•  9 13/16''in
•  Dormer Sleeper Material Thickness
•  1 1/2''in
•  Dormer & Main Roof Plate Line Difference
•  0
•  Dormer Rafter Length
•  84 3/4''in
•  Dormer Sleeper Bevel Length
•  4 7/16''in
•  Dormer Miter Cut Angle
•  19.65382°
•  Dormer Rafter Miter Cut Length
•  28 1/4''in
•  Dormer Intercept Run
•  82 1/4''in
•  Main Roof Slope Intercept Length
•  29 3/4''in
•  Dormer Rafter Length To Main Roof Sheathing Without Sleeper
•  89 1/4''in