A movie theater has a 28 -foot-high screen located 8 feet above your eye level. If you sit $x$ feet back from the screen, your viewing angle, $\theta$, is as given below. \[ \theta=\tan ^{-1} \frac{36}{x}-\tan ^{-1} \frac{8}{x} \] Find the viewing angle, in radians, at distances of 5 feet, 10 feet, 15 feet, 20 feet, 25 feet.

Step 1 ：The problem provides us with a formula for the viewing angle, \(\theta\), at a movie theater screen. The formula is \(\theta = \tan^{-1}\frac{36}{x} - \tan^{-1}\frac{8}{x}\), where \(x\) is the distance from the screen.

Step 2 ：We are asked to find the viewing angle at distances of 5 feet, 10 feet, 15 feet, 20 feet, and 25 feet. We can do this by substituting these distances into the formula for \(\theta\).

Step 3 ：When \(x = 5\) feet, the viewing angle is approximately 0.421 radians.

Step 4 ：When \(x = 10\) feet, the viewing angle is approximately 0.625 radians.

Step 5 ：When \(x = 15\) feet, the viewing angle is approximately 0.686 radians.

Step 6 ：When \(x = 20\) feet, the viewing angle is approximately 0.683 radians.

Step 7 ：When \(x = 25\) feet, the viewing angle is approximately 0.654 radians.

Step 8 ：Final Answer: The viewing angles, in radians, at distances of 5 feet, 10 feet, 15 feet, 20 feet, 25 feet are approximately \(\boxed{0.421}\), \(\boxed{0.625}\), \(\boxed{0.686}\), \(\boxed{0.683}\), \(\boxed{0.654}\) respectively.