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GATE 2020 CE (CE2) – Question 48

Geomatics Engineering · Distance and angle measurement, levelling, traversing, triangulation, total station · 2 marks · Multiple choice

A theodolite at P sees a vane 2 m above the foot of a staff at Q at depression 45°. Horizontal PQ is 20 m. Staff reading at benchmark S of RL 433.050 m is 2.905 m. Neglect curvature and refraction. Find Q reduced level (m).

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

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Correct answer: (B) 413.955

Explanation

Instrument-axis RL is $433.050+2.905=435.955$ m. Vane RL is $435.955-20\tan45^\circ=415.955$ m. Subtract vane height 2 m to obtain **413.955 m, B**.