Projector Math Hurts My Head

[Slimtam]

I'm really hoping that someone can help to simplify this for a dummy like me. I have done lots of research and attempted the online projector calculators, but just can't seem to find the solution here...

I am building a garage sim and have a wall approximately 11' wide x 8' high to place an impact screen. I was thinking of going with an impact screen of 10' x 7'7" which appears to be a standard size and gives me a 4:3 ratio.

So I am trying to determine a decent budget projector to purchase that will allow the image to fill the whole screen nicely as shown in the photo. I'd prefer not to have black bars or unused space on the sides of the image.

But this is where I'm getting lost. I am not sure how the dimensions and aspect ratio of the screen equate to resolution or pixel count... Could someone help here? Or perhaps make a suggestion of a decent budget projector (+/-$500-600 Canadian)?

Save me from my hell. Thanks.

[preludesam]

You can use any 1080p 16:9 projector and use a custom resolution in Windows to make it fit. Leave the projector on auto or 16:9 aspect ratio and place the projector so the top and bottom of the image fills the screen do not worry about the sides. Set a custom resolution in Windows to trim the sides and not squish or stretch the image.

You’re asking a lot for a decent projector at that price. Might want to check the used market. The one pictured is probably quadruple if not more the price you listed.