Chapter 7.1, Problem 86AE

Movie Theater Screens Suppose that a movie theater has a screen that is 28 feet tall. When you sit down, the bottom of the screen is 6 feet above your eye level. The angle formed by drawing a line from your eye to the bottom of the screen and another line from your eye to the top of the screen is called the viewing angle. In the figure, $\theta$ is the viewing angle. Suppose that you sit $x$ feet from the screen. The viewing angle $\theta$ is given by the function $\theta (x)={\tan }^{-1}\left(\frac{34}{x}\right)-{\tan }^{-1}\left(\frac{6}{x}\right)$.

What is your viewing angle if you sit 10 feet from the screen? 15 feel? 20 feel?

If there are 5 feet between the screen and the first row of seats and there are 3 feet between each row and the row' behind it. which row results in the largest viewing angle?

Using a graphing utility, graph $\theta \left(x\right)={\tan }^{-1}\left(\frac{34}{x}\right)-{\tan }^{-1}\left(\frac{6}{x}\right)$.

What value of $x$ results in the largest viewing angle?