--- title: "Triangulation, trilateration; specifications" subject: "Surveying I" chapter: 8 key: "semester_3/surveying_i:triangulation-trilateration-specifications" source: https://www.bctengineer.com/q/semester_3/surveying_i/triangulation-trilateration-specifications site: BCT Engineering --- # Triangulation, trilateration; specifications Surveying I · Chapter 8: Triangulation and Trilateration - Asked in: 2081 Bhadra, 4 marks; 2078 Bhadra, 4 marks; 2074 Chaitra, 4 marks; 2066 Bhadra, 8 marks; 2067 Asar, 8 marks (asked 5 times) - Video: [Triangulation & Trilateration Theory | Difference betn Triangulation & Trilateration | Prashant YT |](https://www.youtube.com/watch?v=XAEiXzEuQtY) — Prashant YT - 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-specifications - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-8 ## Question What is triangulation and trilateration? Write down the general specifications of the different orders (types) of triangulation. ## Short answer Triangulation measures one baseline and all angles to compute other sides by the sine rule. Trilateration measures all sides with an EDM and computes angles by the cosine rule. First‑order triangulation: sides 30–150 km, baseline 5–15 km, average triangle closure <1″. Second‑order: sides 8–30 km, baseline 1.5–5 km, closure 3″. Third‑order: sides 1.5–10 km, baseline 0.5–3 km, closure 6″. ## 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. #### Principle 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) is then 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 the different orders of triangulation | Item | First order (primary) | Second order (secondary) | Third order (tertiary) | |---|---|---|---| | Length of base line | 5 to 15 km | 1.5 - 5 km | 0.5 - 3 km | | Length of sides of triangles | 30 - 150 km | 8 - 30 km | 1.5 - 10 km | | Average triangular error (closure) | less than 1" | 3" | 6" | | Maximum triangular error | 3" | 8" | 12" | | Probable error of base line | 1 in 1,000,000 | 1 in 500,000 | 1 in 250,000 | | Discrepancy between two measures of the base | 5 mm $\sqrt{K}$ | 10 mm $\sqrt{K}$ | 20 mm $\sqrt{K}$ | | Probable error of computed distances | 1 in 60,000 to 1 in 250,000 | 1 in 20,000 to 1 in 50,000 | 1 in 5,000 to 1 in 20,000 | ($K$ is the distance in km. The figures are the common textbook values; Survey Department practice may differ slightly.) Primary (first order) triangulation gives the main control of a country, secondary triangulation fills in the primary net, and tertiary triangulation provides closely spaced stations for engineering and topographic surveys. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What distinguishes triangulation from trilateration? A. Triangulation measures a base and angles; trilateration measures all sides with EDM B. Triangulation measures all sides; trilateration measures angles C. Both measure only one base line D. Triangulation uses levels; trilateration uses chains Answer: A. Triangulation fixes stations by angles from a base line; trilateration by measured sides. (Key point: Definitions) 2. Why is a second base line (check base) measured at the end of a chain? A. To start the next chain B. Its measured length is compared with the computed length to show the accuracy C. To find the elevation of stations D. To avoid measuring azimuth Answer: B. The difference between measured and computed check base shows the accumulated error. (Key point: Check base) 3. How do the base lengths compare for first, second and third order? A. First 0.5-3 km, second 1.5-5 km, third 5-15 km B. All three are 5-15 km C. First 5-15 km, second 1.5-5 km, third 0.5-3 km D. First 1.5-5 km, second 5-15 km, third 0.5-3 km Answer: C. Higher order work uses longer, more accurately measured bases. (Key point: Orders compared) 4. What is the role of tertiary triangulation? A. Gives the main control of a country B. Fills in the primary net only C. Is used only for the check base D. Provides closely spaced stations for engineering and topographic surveys Answer: D. Primary gives national control; secondary fills in; tertiary serves local engineering work. (Key point: Role of orders) ## Related in Surveying I - [Triangulation principle; 1st order trilateration](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-principle-first-order-trilateration) — Surveying I, chapter 8 - [Trilateration over triangulation; primary specs](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atrilateration-advantages-primary-triangulation) — Surveying I, chapter 8 - [Triangulation versus trilateration](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-vs-trilateration) — Surveying I, chapter 8, asked 7× - [Triangulation; EDM principle for trilateration sides](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-and-edm-principle-trilateration) — Surveying I, chapter 8 - [Principle of triangulation and trilateration](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprinciple-triangulation-trilateration-note) — Surveying I, chapter 8 - [Triangulation, trilateration, graphical intersection](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-trilateration-graphical-intersection-pt) — Surveying I, chapter 8 ## Related in other subjects - [Techniques of writing specifications](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Aspec-writing-techniques) — Construction Management, chapter 12, asked 5×