--- title: "Triangulation, trilateration, graphical intersection" subject: "Surveying I" chapter: 8 key: "semester_3/surveying_i:triangulation-trilateration-graphical-intersection-pt" source: https://www.bctengineer.com/q/semester_3/surveying_i/triangulation-trilateration-graphical-intersection-pt site: BCT Engineering --- # Triangulation, trilateration, graphical intersection Surveying I · Chapter 8: Triangulation and Trilateration - Asked in: 2072 Chaitra, 6 marks - Video: [Triangulation Surveying-Part 1](https://www.youtube.com/watch?v=wy6leHTQ0ig) — Civil Engineering Fanatics - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/triangulation-trilateration-graphical-intersection-pt - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-8 ## Question Explain triangulation, trilateration and graphical intersection in plane tabling. ## Short answer Triangulation measures a baseline and all angles, computing sides by the sine rule. Trilateration measures all sides with EDM and computes angles by the cosine rule. Graphical intersection is a plane table method: a point is plotted by drawing sight rays from two plotted stations along a known baseline; the intersection of the rays gives the point's position without measuring any distance. ## Answer **Triangulation** is a method of horizontal control survey in which control stations are fixed at the vertices of a chain or net of triangles. One side (the **base line**) is measured very accurately, all the angles of the triangles are measured, and the lengths of the other sides are computed with the sine rule. **Trilateration** is the method in which the lengths of **all the sides** of the triangles are measured directly with an EDM (electromagnetic distance measuring) instrument, and the angles are computed from the sides using the cosine rule. #### Graphical intersection in plane tabling Graphical intersection is the plane table method in which a point is located by drawing rays to it from two plotted stations at the ends of a base line, and marking the point at the intersection of the rays. No distance to the point needs to be measured. 1. Set the table at A, level it, centre and orient it; plot **a** and the base line ab to scale. 2. Sight the point P from a and draw the ray. 3. Shift to B, orient the table by back-sighting along ba, sight P and draw the ray from b. 4. The two rays meet at **p**, the plotted position of P. A third ray from another station checks it. ```text p / | \ / | \ a ---------- b ``` Graphical intersection is the same idea as triangulation (the point is fixed by two angles from a known base), done graphically instead of by computation. | Basis | Triangulation | Trilateration | Graphical intersection | |---|---|---|---| | Measured | Base and angles | All sides | Base only (plotted) and ray directions | | Method | Computed by sine rule | Computed by cosine rule | Drawn with alidade | | Accuracy | High | High | Low (drawing accuracy) | | Use | Control survey | Control survey | Detailing small areas | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is point P located by graphical intersection in plane tabling? A. By measuring the distance to P with a chain B. By a single ray and a distance C. By back-sighting only D. By drawing rays to P from two plotted stations and marking where they meet Answer: D. Rays from both ends of the plotted base meet at p; no distance is measured. (Key point: Graphical intersection) 2. At the second station B, how is the table oriented? A. By back-sighting along ba B. By compass only C. By sighting P first D. It need not be oriented Answer: A. Back-sighting along line ba orients the table before sighting P. (Key point: Orientation at second station) 3. Which pairing is correct? A. Triangulation: all sides; trilateration: angles B. Triangulation: base and angles, sine rule; trilateration: all sides, cosine rule C. Both use only angles D. Triangulation uses cosine rule; trilateration uses sine rule Answer: B. Triangulation measures base and angles and uses the sine rule; trilateration measures all sides. (Key point: Triangulation vs trilateration) 4. Why is graphical intersection less accurate than triangulation? A. It uses EDM B. It uses a longer base C. It is limited by drawing accuracy D. It uses more rays Answer: C. It is a drawn method, suitable for detailing small areas rather than control. 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