--- title: "Triangulation principle; 1st order trilateration" subject: "Surveying I" chapter: 8 key: "semester_3/surveying_i:triangulation-principle-first-order-trilateration" source: https://www.bctengineer.com/q/semester_3/surveying_i/triangulation-principle-first-order-trilateration site: BCT Engineering --- # Triangulation principle; 1st order trilateration Surveying I · Chapter 8: Triangulation and Trilateration - Asked in: 2080 Baisakh, 4 marks - Video: [Triangulation // Surveying](https://www.youtube.com/watch?v=ZqNY9B15UM0) — engiNERDing - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/triangulation-principle-first-order-trilateration - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-8 ## Question Explain the principle of triangulation. List out the general specifications of 1st order trilateration. ## Short answer A baseline is measured and angles at its ends to a third point are observed; sides are computed by the sine rule, extending the network. First‑order trilateration: all sides measured with EDM, sides 30–150 km (microwave) or shorter with infrared, accuracy 1 part in 100 000 or better, well‑conditioned triangles, meteorological corrections applied, and closure checked. ## Answer #### Principle of triangulation The base line AB is measured accurately. At A and B the angles to a third station C are measured. In triangle ABC, the sides AC and BC are computed by the sine rule: $$ \frac{AB}{\sin C} = \frac{BC}{\sin A} = \frac{AC}{\sin B} $$ The computed side BC (or AC) then becomes the base for the next triangle BCD, and so on. The whole area is covered by a chain or net of triangles. At the end, a second base line (check base) is measured and compared with its computed length; the difference shows the accuracy of the work. Azimuth is observed at the ends to control the direction. ```text C-----E-----G / \ / \ / \ / \ / \ / \ A-----B-----D-----F base check base ``` #### General specifications of first order trilateration | Item | First order trilateration (usual specification) | |---|---| | Method | All sides measured by EDM (infrared or microwave) | | Length of sides | About 30 - 150 km for primary control with long-range (microwave) EDM; infrared EDM reaches only a few km (up to about 10 to 15 km), so sides are shorter | | Accuracy of distance | 1 part in 100,000 or better (for example $\pm (5\ \text{mm} + 1\ \text{ppm})$) | | Figure | Well-conditioned triangles; all angles between 30 and 120 degrees; braced quadrilaterals or polygons with central points | | Observations | Each side measured in both directions and in at least two sets; temperature, pressure and humidity recorded | | Corrections | Meteorological, instrument constants, slope and reduction to mean sea level | | Check | Closure of the figure and comparison of computed and measured sides | (The first order values follow common geodetic standards; they may be revised by the Survey Department.) *If the paper means first order **triangulation**:* base line 5 to 15 km, sides 30 to 150 km, average triangular error less than 1", maximum triangular error 3", probable error of base 1 in 1,000,000, and probable error of computed distances 1 in 60,000 to 1 in 250,000. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In triangulation, once base AB and angles at A and B are measured, how are sides AC and BC found? A. By the cosine rule using three sides B. By the sine rule in triangle ABC C. By direct chaining of each side D. By plane table intersection Answer: B. AB/sin C = BC/sin A = AC/sin B gives the other sides from the base and angles. (Key point: Sine rule computation) 2. How does the survey extend over the whole area after the first triangle is solved? A. A new base is measured for every triangle B. Only angles are measured, with no sides used C. A computed side becomes the base of the next triangle D. Each triangle is solved independently of the others Answer: C. A computed side such as BC is used as the base of the next triangle BCD, forming a chain or net. (Key point: Propagation of base) 3. What is the purpose of the check base measured at the end of the chain? A. To fix the latitude of the station B. To replace the first base line C. To measure the azimuth D. To compare its measured length with the computed length and judge accuracy Answer: D. The difference between measured and computed check base shows the accuracy of the work. (Key point: Check base) 4. How are sides measured in first order trilateration? A. By EDM, each side in both directions with meteorological records B. By chaining with a steel tape C. By tacheometry D. By plane table rays Answer: A. All sides are measured by EDM, in both directions and several sets, recording temperature, pressure and humidity. 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