The screen in the theatre is 22 ft high and is positioned 10 ft above floor, that is flat. First row of seats is 7 ft from screen and rows are 3 ft apart. You decide to sit in row where you get maximum view, which is, where angle theta subtended by screen at your eyes is a maximum. Assume the eyes are 4 ft above floor, and you sit at the distance x from the screen.
a) Illustrate that Theta = arctan(28/x) - arctan(6/x)
b) Use subtraction formula for tangent to illustrate that Theta = arctan(22x/(x^2) + 168)