That's a 110" diag (96" x 52" 16:9) screen in close to 16:10 format. The Epson 1450 should work, is the least expensive long throw that I could find and can be up 20' lens to screen. It also has the advantage of being a light cannon and 16:10 format. If used or refurbished is in the cards the old Epson 5010/20/30 and many others will also work. You will need to find a way to protect the projector from splashing as I wouldn't put one any where near my pool.
"Smart enough to know better, to old to care" ------ Dedicated Bat Cave Home Theater, JVC RS49U/Mitsubishi HC7900DW Projector, 110" 16:9 Jamestown screen with variable power masking for CIW 2.50:1 to 16:9, Marantz 7009 with 7.1.4 Atmos with Ohm mains,3 DIY Subs (2 15" (1 ported, 1 sealed and a 12" 4th order bandpass), 1 DIY butt kicker, Custom Built HTPC, 18TB DroboFS NAS