Fixing a point by distances from two fixed stations: In field surveying, distances AC and BC are measured from two known stations A and B (with baseline AB known), and point C is plotted by intersecting the two distance arcs. This distance–distance intersection method is generally adopted in which class of work?

Introduction / Context:
There are two classic ways to fix an unknown point using two control stations A and B whose separation AB is known: (1) angle–angle (triangulation by angles) and (2) distance–distance (trilateration). In practical chain surveying, where linear measures are primary, the point C is often fixed by measuring AC and BC and plotting with the known baseline AB. This is commonly grouped under triangulation methods as used in chain surveying frameworks.

Given Data / Assumptions:

• AB (baseline) is known or measured accurately.
• Distances AC and BC are measured in the field.
• Angles are not necessarily observed; plotting is by intersecting arcs with radii AC and BC about A and B.

Concept / Approach:
With AB known, two circles of radius AC and BC centered at A and B will intersect at C (up to a mirror ambiguity resolved by sketch or reconnaissance). This is the essence of distance-based triangulation (often called trilateration). Chain surveying frequently employs such distance geometry because chains/tapes are the principal tools.

Step-by-Step Solution:

Verification / Alternative check:
Where possible, measure an additional tie (e.g., a third distance or an angle) to detect blunders; small triangle misfits reveal measurement issues before plotting is finalized.

Why Other Options Are Wrong:

• Chain surveying: It is the overall method; the specific fixing technique here is distance-based triangulation within chain surveying.
• Traverse method: Based on successive angle and distance around a route, not two-distance intersection from a fixed baseline.
• None: Incorrect because the intersection method is well established in triangulation/trilateration practice.

Common Pitfalls:
Ambiguity between the two mathematical intersections; poor scale or plotting can shift the point. Always use checks or sketches to choose the correct intersection.

Final Answer:
Triangulation (distance-based fixing)