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7.8' ceiling, 50 chairs, 120" screen too big to see whole image?

Our condo social room has a 7.8 foot ceiling.  We have 10 rows of chairs setup.

We got a quote from a vendor for a 120” screen.  (I’m not sure if that 120” was diag or width.)

If 120" was the width, at 16:9 I believe that would mean the height would be 5.6 feet.
For 119” diag measurement, that's a height of 58” (4.8 feet)  and 104” image width.

If my math is correct, even if the screen is mounted as high as possible, it would be:

7.8’ – 5.6’ = 2.2’ from the floor
Or
7.8 – 4.8’ = 3’ from the floor

Since we don't have stadium seating in our social room, my concern is that only the folks in the first row could see the whole screen?  

Since the program would be closed-captioned (with the subtitles at the bottom of the screen), most folks could not see the closed captions.

Based on all of this, what's the largest screen that would make sense?

If we mount the screen as high as possible, would that be bad from a strained neck perspective?

Thanks for any thoughts,
Mike
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I attached a picture of the room to this comment.

Here's a picture of the existing 65" TV.  In this picture, the bottom of screen is presently 50 inches off the ground. Top of screen is 14 inches from the ceiling.  Note: the 50" is from the ground to the actual bottom of the visble TV screen;  (the black thing below the screen is a large speaker.

I'm sitting in row 3.  

There's no reason why the seats couldn't be closer to the TV.

-Mike
social-room-65-inch-tv.JPG
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@Merete, I measured diag myself. The screen is indeed 65 inches.

Presently, it is just a TV (no projector).

Mike
Thank you all.  

I'm going to instruct the staff to raise the screen to the max height (at ceiling), and have the chairs moved closer, and see if there are complaints.

_Mike
Thanks !