Question

a movie theater has a 27 - foot - high screen located 7 feet above your eye level. if you sit x feet back from the screen, your viewing angle, θ, is as given below.
θ = tan^(-1) (34/x) - tan^(-1) (7/x)
find the viewing angle, in radians, at distances of 5 feet, 10 feet, 15 feet, 20 feet, 25 feet.
what is the viewing angle θ, in radians, at the distance 5 feet?
θ ≈ 0.468 radians (round to three decimal places as needed.)

Explanation:

Step1: Substitute x = 5 into formula

$\theta=\tan^{- 1}\frac{34}{5}-\tan^{- 1}\frac{7}{5}$

Step2: Calculate inverse - tangent values

$\tan^{- 1}\frac{34}{5}\approx1.4289$ and $\tan^{- 1}\frac{7}{5}\approx0.9505$

Step3: Find the value of $\theta$

$\theta\approx1.4289 - 0.9505=0.4784\approx0.478$ (rounded to three decimal places)

Answer:

$0.478$