Use inverse functions to determine unknown angles

Joe is anxious for the big game. He couldn't get tickets for the game, but he heard it's being broadcast on a large screen at a local megaplex. Since Joe doesn't want to miss a minute of this game, he decides to check out the megaplex the day before the game.

The megaplex was empty, so Joe was able to take some measurements. He found that the 9 foot high screen is placed on a wall with its base 7 feet above his eye level. Now he just needs to figure out how far away from the wall he needs to stand to get the best view. He'll do thi by maximizing angle ?.

\fHDTV Screen Size Minimum Viewing Distance Maximum Viewing Distance (inches) (feet) (feet) 27 3.4 6.8 32 4.0 8.0 42 5.3 10.5 46 5.8 11 .5 50 6.3 12.5 55 6.9 13.8 60 7.5 15.0 65 8.1 16.3 105 13.1 26.3 155 19.4 38.8