---
title: "Resection methods; trial and error"
subject: "Surveying I"
chapter: 6
key: "semester_3/surveying_i:resection-methods-trial-and-error"
source: https://www.bctengineer.com/q/semester_3/surveying_i/resection-methods-trial-and-error
site: BCT Engineering
---

# Resection methods; trial and error

Surveying I · Chapter 6: Plane Table Survey

- Asked in: 2064 Jestha, 6 marks
- Video: [Plane Table Survey (Part 8- Three point problem method- trial and error technique)](https://www.youtube.com/watch?v=HGRMWkjDWPY) — Start Sustainable Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/resection-methods-trial-and-error
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-6

## Question

What are the methods of resection? Explain briefly how it is solved by the trial and error method.

## Short answer

Resection methods: back‑sight orientation, two‑point (auxiliary station), and three‑point (tracing paper, Bessel’s, trial‑and‑error). In trial‑and‑error, orient roughly, sight three points; the intersection of rays forms a triangle of error. Using Lehmann’s rules, estimate p, re‑orient, and repeat until rays meet at a point.

## Answer

**Resection** is the plane table method of locating the table station P on the sheet by sighting known, already plotted points A, B and C from it and drawing the rays *backwards* through the plotted points a, b, c. It is called the **two-point problem** when only two points are available and the **three-point problem** when three are available.

#### Methods of resection
1. **Resection after orientation by back-sighting** (when the station lies on a line already drawn to a plotted point): the table is oriented along that line, and a ray from another plotted point cuts the line at p.
2. **Two-point problem**, solved with an auxiliary station Q.
3. **Three-point problem**, solved by (a) the mechanical (tracing paper) method, (b) the graphical method (Bessel's), or (c) the trial and error method (Lehmann's).

#### Trial and error method
1. Set up the table at P, level it and orient it by eye or compass as accurately as possible.
2. Pivoting on a, b and c, sight A, B and C and draw the three rays back. If the orientation is wrong, they form a small **triangle of error**.
3. Estimate the position of P (the point p) inside or near the triangle using the rules below. Re-orient the board by placing the alidade along p-a and turning the table until A is sighted.
4. Repeat until the triangle of error reduces to a point. That point is the position of P.

**Lehmann's rules for locating p:**
1. If P lies inside the great triangle ABC, p lies inside the triangle of error; if P lies outside the great triangle, p lies outside the triangle of error.
2. When p is outside, it lies on the *same side* of all three rays, that is, to the right of all of them or to the left of all of them, when looking along each ray towards its station.
3. The distance of p from each ray is proportional to the distance of that station from the table. So p is nearest to the ray of the nearest station and farthest from the ray of the farthest station.

```text
     ray a        ray b
         \      /
          \____/
          /\  /\   <- small triangle
         /  \/  \     of error
      ray c
```

## Check yourself

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

1. What is resection?
   A. Fixing a point by rays from two stations
   B. Locating the table station on the sheet by rays drawn back from known plotted points
   C. Orienting by compass
   D. Measuring a base line
   Answer: B. The unknown is the table position. (Key point: Resection)

2. What is the triangle of error?
   A. The triangle formed by the three stations
   B. The triangle of the base line
   C. The small triangle formed by the three rays when orientation is wrong
   D. A plotting scale error
   Answer: C. With wrong orientation the three rays do not meet at a point. (Key point: Triangle of error)

3. Where does the true point lie relative to the three rays?
   A. Always inside the triangle
   B. On opposite sides of the rays
   C. On the longest ray
   D. On the same side of all three rays
   Answer: D. It is to the right of all or to the left of all rays. (Key point: Lehmann's rule 1)

4. How is the true point positioned relative to the rays?
   A. Nearest to the ray of the nearest object and farthest from the ray of the farthest object
   B. Farthest from the nearest object's ray
   C. Equidistant from all rays
   D. On the ray of the farthest object
   Answer: A. Distance from each ray is proportional to the object's distance from the table. (Key point: Lehmann's rule 2)

## Related in other subjects

- [IRR by trial and error; investment decision](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-trial-error-25000) — Engineering Economics, chapter 3