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GATE 2022 CE (CE1) – Question 24

Geomatics Engineering · Distance and angle measurement, levelling, traversing, triangulation, total station · 1 mark · Multiple choice

A line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m. The corrected horizontal length (in m) of the line PQ will be

  1. 342.52
  2. 349.30
  3. 356.20
  4. 350.70

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Show answer and explanation

Correct answer: (A) 342.52

Explanation

The short tape makes the true slope distance smaller: $L_s=350(49.9/50)=349.3$ m. A slope of 1 in 5 gives $\tan\theta=1/5$.

Thus $L_h=L_s/\sqrt{1+(1/5)^2}=342.5168$ m. **Answer: 342.52 m (A)**. Both tape correction and slope reduction decrease the length.