1.  Pitch Break Shed Roof Rafter Length 
2. Pitch Break Shed Roof Miter Angle (Rake Cut Angle) 
3. Total Pitch Break Run ( Intersection of Shed Roof and Main Roof) 
4. Main Roof Intercept Length 
5. Main Roof Run To Intersection of Main Roof And Shed Roof

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

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

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