How much does a degree tilt impact the height of the centerline?
The centerline of the television will change by the sine of the angle of change times the distance from the television.

In simpler terms, for every 12 inches from the television, a one degree change of angle will drop (or raise) the line by 0.209 inches. Realistically, say a 12 foot viewing distance and a ten degree change of the screen, you get a 24 inch drop of the angle of the line.

Most televisions will have a reasonably wide viewing angle both horizontally and vertically, and allow for leeway in the angling of the screen.