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 your eye and the top of the screen is called the viewing angle. In the figure θ, is the viewing angle. Suppose that you sit x feet from the screen. The viewing angle θ is given by the function

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

(b) If there is 5 feet between the screen and the first row of seats and there is 3 feet between each row, which row results in the largest viewing angle?

(c) Using a graphing utility, graph

What value of x results in the largest viewing angle?

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34 6. tan tan 0(x) 28 feet 6 feet