Plane-table resection (three-point problem) — correct sequence of operations: Rough orientation of the plane table The three rays form a small triangle of error Draw back rays through the three plotted control points Select a point within the triangle so each ray would be equally rotated (clockwise or anticlockwise) The adjusted intersection of the three rays gives the correct station position Choose the correct order.

Introduction / Context:
Three-point resection fixes an unknown plane-table station by sighting three well-defined points already plotted on the sheet. Practical solutions (e.g., Lehmann’s method) refine an initial orientation until the small triangle of error collapses to a point.

Given Data / Assumptions:

• Three control points are clearly visible and plotted.
• Plane table can be rotated about a trial point.
• Equal angular corrections concept is used to remove the triangle of error.

Concept / Approach:
After rough orientation, rays are drawn back from the plotted points toward the ground objects. Imperfect orientation creates a small triangle of error where the rays fail to meet. Choosing a trial point within this triangle and applying equal rotations aligns plotted and ground directions; refining this removes the triangle and fixes the true station.

Step-by-Step Solution:

Verification / Alternative check:
Good geometry (well-spread controls) yields a tiny triangle and rapid convergence; poor geometry causes instability and large corrections.

Why Other Options Are Wrong:
They mix the order; the triangle appears only after rays are drawn, and choosing the trial point comes after recognizing the triangle.

Common Pitfalls:
Controls nearly collinear or acute geometry; these enlarge the triangle and degrade accuracy.

Final Answer:
1, 3, 2, 4, 5