Explore the "viewing angle" of a stadium screen as a function of distance from the screen and other physical dimensions. How do we optimize (maximize) that viewing angle?

Slide the distance [b]d[/b] to alter the viewer's distance from the screen.[br]Slide the [b]height of screen[/b], [b]eyeball height[/b], and [b]vertical displacement[/b] sliders to alter the physical dimensions of the scenario.[br]With a keyboard, you may also select a slider and then use ↑↓→← keys to adjust values. Also holding [i]Shift[/i] key adjusts in smaller increments, while also holding [i]Ctrl[/i] key adjusts in greater increments.[br]Alternately, vary these quantities by just dragging the various points in the graphics region.[br][br]Toggle the various checkboxes to see various ways of analyzing the scenario graphically.[br]At what distance is the viewing angle maximized?[br]This problem may be tackled as a[br][list][*]PreCalculus matter: Use inverse trigonometry to write an equation for the viewing angle as a function of the physical dimensions. Use graphing technology to find the maximum point on the relevant graph.[/*][*]Calculus matter: Use derivatives to find the optimal point on the relevant inverse trigonometry function.[/*][*]Geometry matter: Historically, this problem was solved thousands of years before Calculus was developed or electrotonic tools were invented.[/*][/list][br]