The best seat for the viewing angle

A movie theatre screen which is 5 m high has its lower edge 1 m above an observer’s eye. The visual angle $\theta$ of the observer seated $x$ m away is as shown in the diagram below.

(i) Show that $\theta=\tan^{-1}(6/x)-\tan^{-1}(1/x)$.1 mark

(ii) Find the exact distance the observer should sit to obtain the largest visual angle. [You need not establish that the distance gives the largest visual angle.]4 marks

(iii) Suppose that the observer is situated between 2 m and 15 m from the screen. Find, to the nearest degree, the smallest visual angle.2 marks

[2008/RJC/Prelim/I/11(b)]