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The size of the screen should be about 1/3 of your viewing angle to closely match a theater. If you are 20 feet away from the screen (not the projector) you're probably going to need a screen that's closer to 200" diagonal. That's pretty huge and going to limit your projector and placement choices.

Projector Central has good distance and screen size calculators on their site.
 

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Okay, well, I'm going to guess you're pretty well off financially. You're going to need it to afford a 2.35:1 projector that will fill a 240" screen from 20' away even in a completely light-controlled environment. You won't be able to purchase a regular consumer-grade projector and might want to talk to some local commercial installers. Projector Central does review commercial theater projectors as well.
 

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I was just guessing the INFOCUS 777 with an add on anamorphic lens .
That looks like a good candidate, but it is 720p instead of 1080p. At 20' from a 240" screen, I'd suggest going with 1080p if you can. Projector Central says you'll need a higher gain screen though, like 1.3 but that might be based off the spec'ed lumens instead of measured lumens since they didn't review the unit.

Here are the 1080p projectors suitable for a 240" screen according to Projector Central. I'd probably only pick the ones on top, which have the higher wattage bulbs.
 
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