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?
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AChain surveying
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BTraverse method of surveys
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CTriangulation (distance-based fixing)
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DNone of these
Answer
Correct Answer: Triangulation (distance-based fixing)
Explanation
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:
Measure baseline AB as accurately as possible.Measure AC and BC to the target detail point C.On the plan, draw circles with radii equal to scaled AC and BC about A and B.Mark the intersection matching the field situation as point C.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)