$(8$ points$)$ An auditorium with a flat floor has a large screen on one wall. The lower edge of the screen is $5$ feet above eye level and the upper edge of the screen is $20$ feet above eye level.

How far from the screen should you stand to maximize your viewing angle?

HINT: You may use the formula:

$(x)=ta{n}^{-1}(\frac{20}{x})-ta{n}^{-1}(\frac{5}{x}).$

A$.5$ feet away

B$.5\sqrt[\phantom{2}]{2}$ feet away

C$.10$ feet away $($CORRECT$)$

$10\sqrt[\phantom{2}]{2}$ feet away

E$.15$ feet away