GATE 2019 CE (CE1) – Question 53
A staff rests on a benchmark of RL 100.000 m. A theodolite is placed 50 m horizontally from it. Vertical angles from horizontal to staff readings 0.400 m and 2.400 m are found to be the same. Instrument height is 1.400 m. Find RL of the theodolite station (m), to three decimal places.
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Correct answer: 100 to 100
Explanation
The intended reading is opposite vertical angles with equal magnitudes. The instrument axis lies midway between staff marks, at reading $(0.400+2.400)/2=1.400$ m. Its RL is 101.400 m; subtracting instrument height 1.400 m gives station RL **100.000 m**. Literally equal signed angles to two distinct marks would be impossible; this qualification preserves the source wording and keyed interpretation.