Chaining on Slopes – When Can Slope Correction Be Neglected in Practice? Under typical site accuracy requirements, the slope-to-horizontal correction in chaining can be ignored in which of the following practical cases?

Introduction:
Distance measured on a slope exceeds the corresponding horizontal projection. Reducing slope distances to horizontal improves accuracy, but for small slopes the correction may be negligible relative to instrument and reading limits. This question asks when it is acceptable to ignore the correction in routine work.

Given Data / Assumptions:

• Small-slope scenarios: less than about 3° or gradient near 1 in 19.
• Required accuracy is typical of ordinary chaining, not geodetic surveys.
• Line lengths are modest so that cumulative effect remains within tolerance.

Concept / Approach:

For small slope angle θ, horizontal distance H ≈ s * cos θ ≈ s * (1 − θ^2/2). The fractional error is about θ^2/2 in radians. At θ ≈ 3° ≈ 0.0524 rad, θ^2/2 ≈ 0.00137, or about 1.37 mm per metre (1.37 m per kilometre). For short runs in ordinary work, this can fall within permissible error, justifying neglect of the correction.

Step-by-Step Solution:

Verification / Alternative check:

A quick check for a 100 m line at 3°: reduction ≈ 0.137 m. If this exceeds tolerance for your task, apply correction; otherwise, many field handbooks accept ignoring it below this threshold for rough work.

Why Other Options Are Wrong:

'Neither' is incorrect because both listed small-slope cases are typical thresholds; 'exactly zero' is unnecessarily restrictive.

Common Pitfalls:

Ignoring correction on steeper slopes; forgetting that cumulative error over many segments can become significant even if each is small.

Final Answer:

Both (a) and (b)