All the right triangles are similar. If we let x represent the long side of the medium triangle (the distance from the top of the screen to the 5.7 ft height), then you have
.. x/11 = 11/5.7
.. x = 11²/5.7 = 21.2
Since the bottom of the screen is 0.3 ft higher than 5.7 ft, the height of the screen is
.. 21.2 ft - 0.3 ft = 20.9 ft