GATE CE 2016 Set 1 — Question 65
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Geomatics Engineering → Levelling → Trigonometric Levelling
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Question
The vertical angles subtended by the top of a tower at two instrument stations set up at and , are shown in the figure. The two stations are in line with the tower and spaced at a distance of m. Readings taken from these two stations on a leveling staff placed at the benchmark ( m) are also shown in the figure. The reduced level of the top of the tower (expressed in m) is _________
Correct answer
476.5 to 477.5
Solution
1.Identify the Height of Instrument () for both stations:
The staff is placed at the Benchmark () with m.From the diagram, the line of sight from station gives a staff reading m.
The line of sight from station gives a staff reading m.
m
m
2.Set up the trigonometric equations:
Let be the horizontal distance from station to the tower .The distance from station to the tower is m.
Let be the reduced level of the top of the tower.
From station :
From station :
3.Solve for :
m
4.Calculate :
mFinal answer is approximately m, which falls within the range .
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