---
title: "Direction theodolite, least count 6″, station D"
subject: "Surveying I"
chapter: 7
key: "semester_3/surveying_i:direction-theodolite-ls-6-sec-station-d"
source: https://www.bctengineer.com/q/semester_3/surveying_i/direction-theodolite-ls-6-sec-station-d
site: BCT Engineering
---

# Direction theodolite, least count 6″, station D

Surveying I · Chapter 7: Transit and Theodolite

- Asked in: 2067 Asar, 3+5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/direction-theodolite-ls-6-sec-station-d
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-7

## Question

A direction theodolite with a least count of 6 seconds is set over station D to measure directions to stations C, B and A. The observed directions from that position are as follows:

| Stations | Telescope | Horizontal Circle Readings |
|---|---|---|
| C | Direct | 00°00′00″ |
| | Reversed | 179°59′48″ |
| B | Direct | 83°06′48″ |
| | Reversed | 263°06′36″ |
| A | Direct | 242°35′24″ |
| | Reversed | 62°35′12″ |

Compute an abstract of average direction of CD, CB and CA and compute the average angles of CDB, BDA and ADC.

## Short answer

Mean direction from D: to C = 0°00′00″, to B = 83°06′48″, to A = 242°35′24″. Angles from differences: CDB = 83°06′48″, BDA = 159°28′36″, ADC = 117°24′36″; sum 360°, horizon closed.

## Answer

**Method.** A direction theodolite (least count 6″) reads directions on a fixed circle. At D, the directions to C, B and A are observed on both faces. The mean direction of each = [Direct + (Reversed - 180°)]/2. All directions are then referred to C (the reference object) by subtracting the mean direction of C, which gives the abstract of average directions. The angles are the differences between the directions.

#### Abstract of average directions (at D)
| Station | Telescope | Circle reading | Reading ∓ 180° | Mean direction | Direction relative to C (C = 0°) |
|---|---|---|---|---|---|
| C | Direct | 00°00′00″ | | | |
| | Reversed | 179°59′48″ | 359°59′48″ | 359°59′54″ | **0°00′00″** |
| B | Direct | 83°06′48″ | | | |
| | Reversed | 263°06′36″ | 83°06′36″ | 83°06′42″ | **83°06′48″** |
| A | Direct | 242°35′24″ | | | |
| | Reversed | 62°35′12″ | 242°35′12″ | 242°35′18″ | **242°35′24″** |

The reduced average directions are: DC = 0°00′00″, DB = 83°06′48″, DA = 242°35′24″.

#### Average angles
$$
\begin{aligned}
\angle CDB &= 83°06′48″ - 0 = 83°06′48″\\
\angle BDA &= 242°35′24″ - 83°06′48″ = 159°28′36″\\
\angle ADC &= 360^\circ - 242°35′24″ = 117°24′36″
\end{aligned}
$$

Check: 83°06′48″ + 159°28′36″ + 117°24′36″ = 360°00′00″, so the horizon closes.

**Answer:** average directions DC = 0°00′00″, DB = 83°06′48″, DA = 242°35′24″; average angles CDB = 83°06′48″, BDA = 159°28′36″, ADC = 117°24′36″.

## Check yourself

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

1. How is the mean direction to a target found from the two face readings?
   A. [Face L + (Face R -/+ 180°)] / 2
   B. Face L + Face R
   C. Face L - Face R
   D. (Face L + Face R) / 360°
   Answer: A. Face R differs from Face L by 180°, so it is brought back by 180° and averaged with Face L. (Key point: Mean direction formula)

2. How are directions referred to C, the reference object?
   A. Direct readings are added to Reversed readings
   B. The mean direction of C is subtracted from every mean direction, so C = 0°00′00″
   C. 180° is added to each direction
   D. Only the Reversed readings are used
   Answer: B. In the abstract of directions all directions are taken relative to the reference object. (Key point: Referring to C)

3. With DB = 83°06′48″ and DA = 242°35′24″, angle BDA is:
   A. 325°42′12″
   B. 117°24′36″
   C. 159°28′36″
   D. 83°06′48″
   Answer: C. 242°35′24″ - 83°06′48″ = 159°28′36″. (Key point: Angle BDA)

4. How is angle ADC obtained, and what is the check?
   A. 242°35′24″ - 180°; the angles total 180°
   B. 242°35′24″ + 83°06′48″; the angles total 540°
   C. 180° - 242°35′24″; the angles total 360°
   D. 360° - 242°35′24″ = 117°24′36″; the three angles total 360°
   Answer: D. The line DA to DC closes the horizon, so the three angles add to 360°. (Key point: Angle ADC and check)

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