Question about lens selection

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We are installing a 10,000 lumens 4:3 projector in a large room. The image will be a 14' animated sun/moon (that is all the info I have).

The question is lens selection, there is a 3.1 - 4.6 lens available: I'm guessing the video will be almost "full screen" so thinking the screen will be 15' wide.

How far back would the projector be? Is it as easy as 4.6 X 15' = 69'

(69' sounds like a lot).

Thanks for any help!
 
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