Slope correction for a 3° slope over 100 m: compute the subtractive correction A line is measured along a 3° slope with a tape; the sloping distance recorded is 100 m. What is the slope correction C_s (to be subtracted from 100 m) to obtain the horizontal distance?

Introduction / Context:
When measuring distances on sloping ground, field parties often measure along the slope (for speed) and then correct to the required horizontal distance. The correction depends on the slope angle and the measured sloping length. This item asks you to compute the exact subtractive correction for a 3° slope over a measured 100 m line.

Given Data / Assumptions:

• Sloping length l = 100 m.
• Slope angle θ = 3°.
• Horizontal distance L_h = l * cos θ.
• Slope correction C_s = L_h − l (a negative number), which is commonly quoted as a subtractive correction to the recorded length.

Concept / Approach:

For an angle θ, the exact relationship is L_h = l * cos θ. Therefore, the subtractive correction is C_s = l * cos θ − l = l (cos θ − 1). Many references report the magnitude |C_s| = l (1 − cos θ) and note that it must be subtracted from l to obtain L_h.

Step-by-Step Solution:

Verification / Alternative check:

Using the approximate small-angle form C_s ≈ − l * (θ^2 / 2) with θ in radians (θ ≈ 0.05236 rad) gives −100 * (0.05236^2 / 2) ≈ −0.137 m, confirming the exact computation.

Why Other Options Are Wrong:

−0.11 m and −0.12 m are underestimates; −1.87 m is far too large and corresponds to a very steep slope, not 3°.

Common Pitfalls:

Using degrees inside radian-based approximations; forgetting that the correction is subtractive; rounding too early.

Final Answer:

−0.137 m