GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

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