Lean to roof design
 

I want to put up a laen to roof but the pitch is to low under a window so I need to square it off under the window. How do I do this.

you will have to put a window nook in the the roof to either side of the window and level out from the bottom of the window for the flat part of the nook. this nook will need rubber roofing or something similar because it will be flat as compared to the shed roof. usually a double rafter goes on either side of the window and the flat roof is built between the two doubles and tied back to the house andf flashed under the window. A call it a flat roof but it will need some slope for water to flow away from the house/window, just not as much slope as the shed roof has

how high do you suppose the shed roof will land above the bottom of the window?

Might it be better to pitch it to the two sides and have a peak in the center? Depending on location of window and height from top of wall of addition it may give you a better slope.