A theodolite was set up at a station $P$. The angle of depression to a vane $2\ m$ above the food of a staff held at another station $Q$ was $45^\circ$. The horizontal distance between stations $P$ and $Q$ is $20\: m$. The staff reading at a benchmark $S$ of $RL\: 433.050\: m$ is $2.905\: m.$ Neglecting the errors due to curvature and refraction, the $RL$ of the station $Q\: \text{(in m)},$ is

1. $413.050$
2. $413.955$
3. $431.050$
4. $435.955$