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GATE 2016 CE (CE1) – Question 65

Geomatics Engineering · Distance and angle measurement, levelling, traversing, triangulation, total station · 2 marks · Numerical answer

The vertical angles subtended by the top of a tower T at two instrument stations set up at P and Q, are shown in the figure. The two stations are in line with the tower and spaced at a distance of 60 m. Readings taken from these two stations on a leveling staff placed at the benchmark (BM = 450.000 m) are also shown in the figure. The reduced level of the top of the tower T (expressed in m) is _________

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Correct answer: 476.500 to 477.500

Explanation

Instrument levels are450.000+0.555=450.555m at P and450.000+2.555=452.555m at Q. Let x be the horizontal distance from Q to the tower. Equate top levels:452.555+x tan16.5°=450.555+(x+60)tan10.5°. Solving and substituting gives **476.921m**; different instrument heights must be retained.