Question:
A 50 m tape is held 2 m out of line, then its true length is:
A 50 m tape is held 2 m out of line, then its true length is:
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When measuring with tape held out of alignment, compute horizontal distance using:
\[
\text{True length = \sqrt{(\text{Tape length)^2 - (\text{Offset)^2
\]
Updated On: May 27, 2025
- 49.96 m
- 48.96 m
- 49.02 m
- 48.02 m
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The Correct Option is A
Solution and Explanation
Step 1: Visualizing the error.
When the tape is 2 m off from the straight line, it forms a right triangle:
Hypotenuse = tape = 50 m
One leg = lateral offset = 2 m Adjacent leg = true length (horizontal distance)
Step 2: Apply Pythagoras theorem: \[ \text{True length} = \sqrt{50^2 - 2^2} = \sqrt{2500 - 4} = \sqrt{2496} \approx 49.96 \text{ m} \]
When the tape is 2 m off from the straight line, it forms a right triangle:
Hypotenuse = tape = 50 m
One leg = lateral offset = 2 m Adjacent leg = true length (horizontal distance)
Step 2: Apply Pythagoras theorem: \[ \text{True length} = \sqrt{50^2 - 2^2} = \sqrt{2500 - 4} = \sqrt{2496} \approx 49.96 \text{ m} \]
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