Concept:
Triangulation is a control survey in which a network of well conditioned triangles is laid out, the angles are measured precisely and the lengths of all sides are computed from one or more measured baselines. Its purpose is to provide accurate horizontal control.
Step 1:
Recall the recognised objectives of triangulation: to establish accurate control for plane and geodetic surveys and for photogrammetric mapping of large areas, to fix accurate positions of points in engineering projects, and to monitor movements such as crustal or structural deformation.
Step 2:
Compare each option with these objectives. Options (1), (2) and (4) are standard objectives of triangulation. Determining the earth's curvature correction is a computational reduction applied in levelling and geodetic computations, not an objective of carrying out a triangulation survey.
Answer: Option (3) — Determination of earth's curvature correction.