SOLUTION

(Diagam not to scale)

We define θ₁ and θ₂ as shown in the diagram.

So θ = θ₂ - θ₁. [See diagram]

Let x be the distance from directly under the screen to the observer. To maximise θ , we will need to find

and then set it to 0.

We note that

This gives:

Now since θ = θ₂ - θ₁,

We have a function of a function in each term.

Now, in the first term, if we let

then

Similarly for the second term, we will have:

So we have:

To find when this equals 0, we need only determine when the numerator is 0.

That is

-2.4x² + 222.36 = 0

This occurs when x = 9.63 (we take positive case only)

So the observer must be 9.63 m from directly below the screen to get the best view.