GATE CE 2022 Set 1 — Question 24
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Geomatics Engineering → Distance & Angle Measurement → Errors in Measurement
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Question
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
Correct answer
(A) 342.52
Solution
Step 1: Correct the measured slope length for the tape error.
Nominal length of tape () = 50 m
Actual length of tape () = m
Measured slope length () = 350 m
Corrected slope length () = mStep 2: Calculate the horizontal length from the corrected slope length.
The slope is 1 in 5 (vertical : horizontal). Let the horizontal distance be and vertical be . Then .
The slope distance .
We have the corrected slope distance m.
Horizontal length m.
Rounding to two decimal places, we get 342.52 m. The correct option is (A).
Nominal length of tape () = 50 m
Actual length of tape () = m
Measured slope length () = 350 m
Corrected slope length () = mStep 2: Calculate the horizontal length from the corrected slope length.
The slope is 1 in 5 (vertical : horizontal). Let the horizontal distance be and vertical be . Then .
The slope distance .
We have the corrected slope distance m.
Horizontal length m.
Rounding to two decimal places, we get 342.52 m. The correct option is (A).
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