Given two angles of elevation, find height

Question

From a ship at sea, the angle of elevation of the top and bottom of a vertical lighthouse standing on the edge of a vertical cliff are $33^{\circ}$ and $28^{\circ}$, respectively. If the lighthouse is $20$ units high, calculate the height of the cliff.
Here's the diagram I came up with. I am not sure what to do next.

Answer 1

In $\Delta SQR$, $$\tan 28°=\frac{QR}{SR}\Rightarrow SR=\frac{QR}{\tan 28°}$$ and in $\Delta SPR$, $$\tan 33°=\frac{PR}{SR}\Rightarrow SR=\frac{PR}{\tan 33°}.$$ $\therefore QR\tan 33°=PR\tan 28°\\ \Rightarrow QR\tan 33°=(PQ+QR)\tan 28°\\ \Rightarrow QR~(\tan 33°-\tan 28°)=20\tan 28°$

Now, using $\tan 28°=0.532$ and $\tan 33°=0.649$, we get $$QR=\frac{20\times0.532}{0.649-0.532}=90.940\mathrm{~~~units.}$$ The cliff is of height $90.940$ units.