Chapter 4.7, Problem 127PE

The vertical viewing angle $\theta$ to a movie screen is the angle formed from the bottom of the screen to a viewer's eye to the top of the screen. Suppose that the viewer is sitting $x$ horizontal feet from an IMAX screen $53$ ft high and that the bottom of the screen is $10$ vertical feet above the viewer's eye level. Let $a$ be the angle of elevation to the bottom of the screen.

a. Write an expression for $\tan \alpha$ .

b. Write an expression for $\tan \left(\alpha +\theta \right)$ .

c. Using the relationships found in parts (a) and (b), show that $\theta ={\tan }^{-1}\frac{63}{x}-{\tan }^{-1}\frac{10}{x}$ .