2017 THREE(d)

A building has an external elevator. The elevator is rising at a constant rate of $2\mathrm{m}{\mathrm{s}}^{-1}$.

Sarah is stationary, watching the elevator from a point $30\mathrm{m}$ away from the base of the
elevator shaft.

Let the angle of elevation of the elevator floor from Sarah's eye level be $\theta$.

Find the rate at which the angle of elevation is increasing when the elevator floor is $20\mathrm{m}$
above Sarah’s eye level.

*You must use calculus and show any derivatives that you need to find when solving this
problem.*