---
title: "Principle of triangulation and trilateration"
subject: "Surveying I"
chapter: 8
key: "semester_3/surveying_i:principle-triangulation-trilateration-note"
source: https://www.bctengineer.com/q/semester_3/surveying_i/principle-triangulation-trilateration-note
site: BCT Engineering
---

# Principle of triangulation and trilateration

Surveying I · Chapter 8: Triangulation and Trilateration

- Asked in: 2074 Asoj, 4 marks
- 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/principle-triangulation-trilateration-note
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-8

## Question

Write a short note on the principle of triangulation and trilateration.

## Short answer

In triangulation, a baseline is measured; all angles of the triangle network are observed, and remaining sides are computed using the sine law, with a check baseline at the end. Trilateration measures all sides of each triangle with EDM, then computes angles via the cosine law, eliminating the need for angle observations or baseline extension.

## 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) 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
```

#### Principle of trilateration
If the three sides a, b, c of a triangle ABC are measured, any angle is found with the cosine rule:

$$
\cos A = \frac{b^2 + c^2 - a^2}{2bc}
$$

The sides are measured by EDM, so no angles are observed and no base line extension is needed. The figure is solved from the lengths alone.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which quantities are measured in triangulation to solve triangle ABC?
   A. All three angles only
   B. Base AB and angles at A and B
   C. All three sides only
   D. Only angle C
   Answer: B. A base and two angles allow the remaining sides to be found by the sine rule. (Key point: Triangulation principle)

2. Which formula gives angle A in trilateration from sides a, b, c?
   A. sin A = a/b
   B. cos A = (a^2 + b^2 + c^2)/2
   C. cos A = (b^2 + c^2 - a^2)/(2bc)
   D. tan A = a/(b+c)
   Answer: C. The cosine rule gives any angle from the three sides. (Key point: Trilateration formula)

3. What is the key difference in field observation in trilateration?
   A. Only angles are observed
   B. Heights are observed
   C. Nothing is measured
   D. No angles are observed; sides are measured by EDM
   Answer: D. The figure is solved from lengths alone. (Key point: No angles observed)

## 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
- [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
- [Triangulation versus trilateration](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-vs-trilateration) — Surveying I, chapter 8, asked 7×
- [Triangulation, trilateration; specifications](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-trilateration-specifications) — Surveying I, chapter 8, asked 5×
- [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, trilateration, graphical intersection](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-trilateration-graphical-intersection-pt) — Surveying I, chapter 8