Discussion
The back sight of 1.258 m was observed for the bench mark (BM) at reduced level (RL) of 48 m. The corresponding fore sight on the staff held vertically inverted to the underside of a bridge beam is 4.645 m. The RL at the underside of the bridge beam in m is
Answer: D
The RL of the underside of the beam is 53.903 m.
The height of instrument is the bench mark's RL plus the back sight. A staff held upside down against an overhead point is read as a negative staff reading, so the inverted fore sight is added to the height of instrument instead of subtracted:
\[ \begin{aligned} HI &= 48 + 1.258 = 49.258 \\ RL &= 49.258 + 4.645 = 53.903 \end{aligned} \]
The point must be above the line of sight, since the staff hangs down from the beam to it. 44.613 subtracts the fore sight as for an ordinary staff held on the ground, which would put the beam below the instrument. 46.936 and 51.581 match no consistent combination of the two readings.
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