Answer:
The viewing angles are as follows:
For x=5 feet, θ = 0.529 radians
For x=10 feet, θ = 0.708 radians
For x=15 feet, θ = 0.726 radians
For x=20 feet, θ = 0.691 radians
For x=25 feet, θ = 0.640 radians
Step-by-step explanation:
The viewing angle is given as:
θ = tan⁻¹(30/x) - tan⁻¹ (6/x)
where x is the distance between you and the screen.
The question is asking us to find the viewing angle θ at various distances. The distance value needs to be substituted in the above equation in place of x. So,
For x=5 feet:
θ = tan⁻¹(30/5) - tan⁻¹ (6/5)
= 1.4056 - 0.8761
θ = 0.529 radians
For x = 10 feet:
θ = tan⁻¹(30/10) - tan⁻¹ (6/10)
= 1.249 - 0.540
θ = 0.708 radians
For x = 15 feet:
θ = tan⁻¹(30/15) - tan⁻¹ (6/15)
= 1.107 - 0.380
θ = 0.726 radians
For x = 20 feet:
θ = tan⁻¹(30/20) - tan⁻¹ (6/20)
= 0.983 - 0.291
θ = 0.691 radians
For x = 25 feet:
θ = tan⁻¹(30/25) - tan⁻¹ (6/25)
= 0.876 - 0.235
θ = 0.640 radians
