Question

In the diagram below, the circle has a diameter that is the length of the screen. Determine a seat that has a viewing angle of 90 deg . Explain your reasoning.

Answer 1

The seat that has a viewing angle of 90 degrees is the seat that is closest to the screen.

The seat that has a viewing angle of 90 degrees is the seat that is closest to the screen because the viewing angle is the angle between the line of sight from the viewer to the center of the screen and a line perpendicular to the screen. The closer the viewer is to the screen, the larger the viewing angle will be.

Viewing angle = 2 *
`tan^-^1`(r/d)

r = the distance from the viewer to the center of the screen

d = the diameter of the screen

We can in the diagram that the distance from the viewer to the center of the screen is equal to the radius of the circle, which is 1/2 the diameter.

Viewing angle = 2 * tan
`^-^1`(1/2 * d / d)

= 2 *
`tan^-^1`(1/2)

= 90 degrees