The conventional wisdom is to centre the screen at the average eyelevel of a seated adult. This eyeline height varies depending on the type of seating and whether folk sit up or slouch, so it's not a one-size-fits-all solution, but it does give a starting point. Seated eye height for the non-slouching crowd is somewhere around 40-42".
This gives us something along the lines of the image below.
When this rule of thumb was devised we'd already moved from CRT TV to flatscreen, but at the time 42" was the norm and 50" was considered large. Screens as large as 80" or bigger just weren't on the horizon at the sort of accessible prices we have today.
If we follow the same rules then for an 80" screen, then the bottom of the screen gets quite a bit closer to the floor. Here, the screen bottom edge is roughly 20" from floor level. In some cases this will work because the furniture and room layout don't impede the image. However, at an 80" diagonal the screen size is getting close to older projector screen dimensions, and for those we used a rule of thumb based on thirds rather than half.
Here's the same screen image height as above, but the bracket position of the wall is shifted up so that eyeline levels up on the 1/3rd-2/3rds border.
Shifting the screen up means that perspective effects come in to play. The top width of the screen will look slightly smaller than the bottom width. We refer to this as keystone distortion. To correct it you would tilt the screen so that the top and bottom edges appear to be the same distance from the viewer. In this case the tilt amount is about 3 degrees.
