---
title: "Triangulation principle; third-order specifications"
subject: "Surveying I"
chapter: 8
key: "semester_3/surveying_i:triangulation-principle-third-order"
source: https://www.bctengineer.com/q/semester_3/surveying_i/triangulation-principle-third-order
site: BCT Engineering
---

# Triangulation principle; third-order specifications

Surveying I · Chapter 8: Triangulation and Trilateration

- Asked in: 2076 Asoj, 4 marks
- Video: [Classification of triangulation || Types of triangulation || Triangulation Survey || advance survey](https://www.youtube.com/watch?v=UpuSu41MhO0) — Mukesh Kumar
- 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-third-order
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-8

## Question

Explain the principle of triangulation. List out the general specification of third order triangulation survey.

## Short answer

Triangulation starts with a measured baseline; angles from its ends to a third station determine the other sides by the sine rule, extending across a network. Third‑order triangulation: sides 1.5–10 km, baseline 0.5–3 km, average triangle closure 6″, maximum 12″, base error 1 in 250 000.

## 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
```

#### General specification of third order (tertiary) triangulation
| Item | Specification |
|---|---|
| Length of base line | 0.5 to 3 km |
| Length of sides of triangles | 1.5 to 10 km |
| Average triangular error (closure) | 6" |
| Maximum triangular error | 12" |
| Probable error of base line | 1 in 250,000 |
| Discrepancy between two measures of the base | 20 mm $\sqrt{K}$ ($K$ in km) |
| Probable error of computed distance | 1 in 5,000 to 1 in 20,000 |

## Check yourself

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

1. What is measured accurately at the start of a triangulation?
   A. All the sides
   B. The base line
   C. Only the azimuth
   D. The area of the net
   Answer: B. One base line is measured accurately, the angles are observed and other sides are computed. (Key point: Principle)

2. Which relation is used to compute the sides?
   A. AB/cos C = BC/cos A
   B. AB sin C = BC sin A + AC
   C. AB/sin C = BC/sin A = AC/sin B
   D. AB^2 = BC^2 + AC^2 always
   Answer: C. The sine rule links each side with the sine of its opposite angle. (Key point: Sine rule)

3. What are the maximum triangular error and base line probable error for third order?
   A. 3" and 1 in 1,000,000
   B. 8" and 1 in 500,000
   C. 6" and 1 in 100,000
   D. 12" and 1 in 250,000
   Answer: D. Third order has maximum triangular error 12" and base line probable error 1 in 250,000. (Key point: Third order specs)

4. Why is a second base line measured at the end of the chain?
   A. To check accuracy by comparing measured and computed lengths
   B. To increase the number of triangles
   C. To find the elevation
   D. To avoid angle measurement
   Answer: A. The check base discrepancy shows how well the work agrees. (Key point: Check base)

## 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, trilateration; specifications](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-trilateration-specifications) — Surveying I, chapter 8, asked 5×
- [Types of triangles; first-order specification](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangle-types-first-order-spec) — 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
- [Principle of triangulation and trilateration](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprinciple-triangulation-trilateration-note) — Surveying I, chapter 8
- [Purposes of triangulation; tertiary triangulation](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-purpose-tertiary) — Surveying I, chapter 8

## Related in other subjects

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- [Third-order difference equation: limit x(k+2)/x(k)](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Athird-order-difference-limit-k) — Digital Control System, chapter 2, asked 2×
- [Second-order non-linear kinematic wave; FDM principle](https://www.bctengineer.com/question.md?key=semester_8%2Fcomputational_techniques_in_civil_engineering%3Asecond-order-nonlinear-kinematic-principle) — Computational Techniques in Civil Engineering, chapter 5