Viewing Angle, Stadium Screen
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?
Stadium Screen Viewing Angle
Slide the distance d to alter the viewer's distance from the screen.
Slide the height of screen, eyeball height, and vertical displacement sliders to alter the physical dimensions of the scenario.
With a keyboard, you may also select a slider and then use ↑↓→← keys to adjust values. Also holding Shift key adjusts in smaller increments, while also holding Ctrl key adjusts in greater increments.
Alternately, vary these quantities by just dragging the various points in the graphics region.
Toggle the various checkboxes to see various ways of analyzing the scenario graphically.
At what distance is the viewing angle maximized?
This problem may be tackled as a
- 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.