We want to add a third car garage to an existing side entry garage with a hip roof. My question is how to we attach the roof to the hip roof making it look nice.
The picture should make it a bit more evident on what we want to do.
I don't know the size or shape and therefore structure of your roof, but I'll presume it's square without any lower peak support. The only way it looks and works good is to fill-in the hips peak to peak. I say hips in plural as you may not want to re-frame the entire roof. You have 3 options.
The 1st is to duplicate the old garage roof on the new garage and then fill-in from peak to peak. This, will allow the 4-ridge beams of each hip roof to support the peak to peak single ridge beam without the need for columns, trusses or built-up beams.
The 2nd is much easier, faster, stronger and less expensive. Re-frame the roof as a single gabled or straight peaked roof. Very easy end cuts only and just some simple beefing-up of the end walls. Yes, you can still hip the ends as a 3rd option, but it gets very complicated and costly...as you'll find if you begin to try the 1st option.
The 3rd and easiest of all is to do a Shed Roof. It's very similar to framing a wall, which will end up being tilted. Tilt it street-side and you maintain privacy while allowing a lot of windows in the rear for a flood of natural light. Tilt it back and you increase the building's scale, for possibly much better curb appeal.