I put the seat boards in place to get a feel for it. Looks like I'll need a third board to make a wider seat.
This is design on-the-fly.

To determine the size of the seat I went around to our various lawn chairs and patio chairs to determine what size was the most comfortable.
I figured that the front edge of the seat had to be about 45 cm off the ground, the seat should go back (width) about 45 cm with a slope of 10 to 1 going down so it goes back 45 cm and drops 4.5 cm. The back height should be 60 cm and slope back 10 to 4. So If I go up 50 cm it slopes back 20 cm. In the end we'll only know how comfortable it is by sitting on it.