Question about adding a shed roof to a 12x12 pitched roof
way too vague, as to the pitch it could be anything you want it to be I will say that 12 pitch will never catch a 12 pitch roof, try a 4 pitch. If you cant set it up using math, return to dumb math-nail a 2X4 to the 8' post to get your soffit distance, nail a board to the existing house fascia to represent the rise you want to establish, get a string and line it up, now you will know where to nail the "ledger" board. To cut the angle and birdsmouth, now you an lay the board on your ledger to span where you want to go and just mark what you want to cut off.
Robert J. Michael Homes, Inc./RJM Build