The screen in a theatre is 22ft high and is positioned 10 ft above the floor which is flat. The first row of seats is 7 ft from the screen and the rows are 3 ft apart. You decide to sit in the row where you get the maximum view, that is, where the angle Ө subtended by the screen at your eyes is a maximum. Suppose your eyes are 4 ft above the floor, and you sit at a distance x from the screen.

(a) Show that Ө= tan-1(28/x) - tan-1(6/x)

Question

The screen in a theatre is 22ft high and is positioned 10 ft above the floor which is flat. The first row of seats is 7 ft from the screen and the rows are 3 ft apart. You decide to sit in the row where you get the maximum view, that is, where the angle Ө subtended by the screen at your eyes is a maximum. Suppose your eyes are 4 ft above the floor, and you sit at a distance x from the screen. 

(a) Show that Ө= tan-1(28/x) - tan-1(6/x)