examday

/TMUA

The points $A$, $B$ and $C$ lie in that order on a horizontal straight line, with $AB=BC=3\,\mathrm{m}$.

A vertical pole of positive height has its base $P$ on this line, distinct from $A$, $B$ and $C$. The angles of elevation of the top of the pole from $A$, $B$ and $C$ are $\alpha$, $\beta$ and $\gamma$, respectively, and

What is the sum of all the distinct possible values of $BP$, in metres?