---
title: "Closed traverse ABCDA, missing data"
subject: "Surveying II"
chapter: 1
key: "semester_4/surveying_ii:closed-traverse-abcda-missing-2069b"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-traverse-abcda-missing-2069b
site: BCT Engineering
---

# Closed traverse ABCDA, missing data

Surveying II · Chapter 1: Traversing

- Asked in: 2069 Bhadra, 8 marks
- Video: [The length and bearings of a closed traverse PQRSP are given in the table.The missing length and](https://www.youtube.com/watch?v=CkQNnP2pZh4) — Unique Series - Civil Mantraa
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-traverse-abcda-missing-2069b
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1

## Question

For a closed traverse ABCDA, compute the missing data.

| Line | Length (m) | Bearing |
|---|---|---|
| AB | 100.00 | N 45°30' W |
| BC | 605.00 | N 5°30' E |
| CD | 95.00 | N 88°20' E |
| DA | ? | ? |

## Short answer

Sum latitudes and departures of AB, BC and CD, then DA must cancel those sums. Length DA is 679.99 m and its whole circle bearing is 186 deg 54 min, or S 6 deg 54 min W.

## Answer

For a closed traverse $\Sigma\text{Lat}=0$ and $\Sigma\text{Dep}=0$, so the missing line DA (length and bearing) is the line that closes the figure formed by AB, BC and CD.

#### Step 1: Whole circle bearings and latitudes, departures
AB = N45°30'W = 314°30', BC = N5°30'E = 5°30', CD = N88°20'E = 88°20'.

$$
\text{Lat}=L\cos\theta,\qquad \text{Dep}=L\sin\theta
$$

| Line | Length (m) | Bearing | Latitude | Departure |
|---|---|---|---|---|
| AB | 100.00 | 314°30' | +70.091 | -71.325 |
| BC | 605.00 | 5°30' | +602.215 | +57.987 |
| CD | 95.00 | 88°20' | +2.763 | +94.960 |
| **Sum** |  |  | +675.069 | +81.621 |

#### Step 2: Length of DA
The latitude and departure of DA must cancel these sums:

$$
\begin{aligned}
\text{Lat}_{DA}&=-(+675.069)=-675.069\ \text{m}\\
\text{Dep}_{DA}&=-(+81.621)=-81.621\ \text{m}\\
L_{DA}&=\sqrt{(-675.069)^2+(-81.621)^2}=679.99\ \text{m}
\end{aligned}
$$

#### Step 3: Bearing of DA
$$
\tan\theta=\frac{\text{Dep}}{\text{Lat}}=\frac{-81.621}{-675.069}\ \Rightarrow\ \theta=186^\circ 54'
$$

Latitude is negative and departure is negative, so DA lies in the south-west quadrant: whole circle bearing = 186°54', i.e. **S 6°54' W**.

#### Check
Lat: +675.069 + (-675.069) = 0.000; Dep: +81.621 + (-81.621) = 0.000, so the traverse closes.

**Answer:** DA = 679.99 m, bearing 186°54' (S 6°54' W).

## Check yourself

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

1. How is the missing line DA obtained?
   A. Its latitude and departure must be equal and opposite to the sums for AB, BC, CD
   B. Its length equals the average of the others
   C. Its bearing equals that of AB reversed
   D. From the angle sum
   Answer: A. For a closed traverse ΣLat = ΣDep = 0. (Key point: Closure principle)

2. What are the WCB of AB (N45°30'W) and CD (N88°20'E)?
   A. 314°30' and 88°20'
   B. 45°30' and 88°20'
   C. 134°30' and 91°40'
   D. 225°30' and 268°20'
   Answer: A. N45°30'W = 360° - 45°30' = 314°30'; N88°20'E = 88°20'. (Key point: Whole circle bearings)

3. ΣLat = +675.069 and ΣDep = +81.621 for AB, BC, CD. What are Lat(DA) and Dep(DA)?
   A. +675.069 and +81.621
   B. -675.069 and -81.621
   C. -675.069 and +81.621
   D. 0 and 0
   Answer: B. They must cancel the sums, so both are of opposite sign. (Key point: Sums of lat and dep)

4. Lat(DA) and Dep(DA) are both negative. What is the bearing of DA?
   A. 6°54' in the NE quadrant
   B. 186°54' (S 6°54' W)
   C. 173°06' (S 6°54' E)
   D. 353°06' (N 6°54' W)
   Answer: B. Both negative puts it in the SW quadrant, tan^-1(81.621/675.069) = 6°54', so WCB 186°54'. (Key point: Quadrant and bearing)

5. How is L_DA calculated and what is its value?
   A. sqrt(Lat^2 + Dep^2) = 679.99 m
   B. Lat + Dep = 756.69 m
   C. Lat x Dep
   D. Average of the other lengths = 266.7 m
   Answer: A. L = sqrt(675.069^2 + 81.621^2) = 679.99 m. (Key point: Length of DA)

## Related in Surveying II

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- [Closed traverse ABCDA missing data, C(1200, 2000)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcda-c-1200-2000) — Surveying II, chapter 1
- [Traverse missing length CD, bearing EA](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-missing-cd-length-ea-bearing) — Surveying II, chapter 1
- [Closed traverse ABCDA missing figures (C=2500)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcda-missing-2072m) — Surveying II, chapter 1
- [Closed traverse ABCDA, B at 26500 N 22400 E](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcda-missing-2066m) — Surveying II, chapter 1
- [Missing bearings of BC and DE in traverse](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-missing-bearings-bc-de) — Surveying II, chapter 1

## Related in other subjects

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- [Local attraction, bearings AB 305°00′ (EA 45°)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ea-305-00) — Surveying I, chapter 4, asked 2×
- [Local attraction: AB 69°30′ compass traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ab-69-30-reordered) — Surveying I, chapter 4
- [Local attraction, S 40°30′ W traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-quadrantal-s40-30w) — Surveying I, chapter 4