The 90 degree angle between the seat and back of a chair is the same if you're 4'5" or 10'1". Use that as a guide. Scootch your butt back up as far as it can go. If you don't normally do this, then expect some discomfort after a bit. Get used to it, and do it the rest of your life. If you have trouble, then try ropes.
If you're looking to strengthen your back, then I suggest getting one of those nifty inflatable exercise balls (a.k.a the Swiss Ball). Rest stomach down on the ball and go nuts. Check out
these videos.