COMEDK · Maths · 27. Application of Derivatives

A movie screen on a wall is 20 feet high and 10 feet above the floor. What is the maximum viewing angle \(\theta\) (in radians) that can be achieved by positioning yourself at the optimal distance from the wall?

A \(\dfrac{\pi}{4}\)
B \(\dfrac{\pi}{2}\)
C \(\dfrac{\pi}{3}\)
D \(\dfrac{\pi}{6}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\dfrac{\pi}{6}\)

Step-by-step Solution

Detailed explanation

Let \(x\) be the distance of the observer from the wall. Let \(\alpha\) be the angle of elevation to the bottom of the screen and \(\beta\) be the angle of elevation to the top of the screen. The height of the bottom of the screen is \(10\) feet and the height of the top of the…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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