Intersection from two transit stations: For locating a distant object visible from two transit (theodolite) stations, which method is usually preferred?

Introduction / Context:When a remote point cannot be occupied or measured directly, its position can be fixed by observations from two known stations. Several combinations of observed quantities are possible, but one is generally most efficient and precise for distant targets.

Given Data / Assumptions:

• The distant point is intervisible from both transit stations.
• Station coordinates or relative position are known.
• Angular measurements are typically more reliable than long-distance linear measures in difficult terrain.

Concept / Approach:Angular intersection uses the measured directions (bearings or angles) to the unknown point from both stations, forming two rays that intersect at the point's position. It avoids the challenges of long EDM/tape distances and often yields higher accuracy with good geometry (wide intersection angles).

Step-by-Step Solution:

Verification / Alternative check:Redundancy by adding a third station or repeating angle sets improves confidence and provides blunder detection.

Why Other Options Are Wrong:

• Angles + distances: Feasible but unnecessary for most cases and costlier.
• Distances only: Requires distance to the remote point from both stations, often impractical.
• Mixed angle/distance: Works but loses the simplicity and robustness of pure angular intersection.

Common Pitfalls:Poor intersection geometry (very acute/obtuse angles) magnifies position error; choose well-spaced stations.

Final Answer:Measure only angles from the two stations (angular intersection)