---
title: "True horizontal distance from slope distances"
subject: "Surveying I"
chapter: 2
key: "semester_3/surveying_i:slope-distances-tape-2cm-long"
source: https://www.bctengineer.com/q/semester_3/surveying_i/slope-distances-tape-2cm-long
site: BCT Engineering
---

# True horizontal distance from slope distances

Surveying I · Chapter 2: Distance Measurements

- Asked in: 2062 Poush, 8 marks
- Video: [Chapter Horizontal Distance : Calculation](https://www.youtube.com/watch?v=usacVKggQD0) — Asraf Heafy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/slope-distances-tape-2cm-long
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-2

## Question

The following slope distances were measured along a chain line with a 30 m tape.

Slope distance (m) = 25.50, 24.60, 28.70, 29.50 and 18.50.

Difference of elevation between ends (m) = 2.50, 5.30, 3.35, 2.50 and 1.50.

It was noted afterwards that the tape was 2 cm too long. Find the true horizontal distance.

## Answer

**Method.** The tape is 30.02 m, 2 cm too long, so every reading is too small. First each slope distance is corrected for tape length, then reduced to horizontal using the height difference $h$:

$$
l' = l\times\frac{30.02}{30},\qquad D = \sqrt{l'^{2} - h^{2}}
$$

| Slope $l$ (m) | $h$ (m) | Corrected slope $l'$ (m) | Horizontal $D$ (m) |
|---|---|---|---|
| 25.50 | 2.50 | 25.5170 | 25.3942 |
| 24.60 | 5.30 | 24.6164 | 24.0391 |
| 28.70 | 3.35 | 28.7191 | 28.5231 |
| 29.50 | 2.50 | 29.5197 | 29.4136 |
| 18.50 | 1.50 | 18.5123 | 18.4515 |
| Total | | | 125.8215 |

(The total measured slope length is 126.80 m.)

**Answer: true horizontal distance $= 125.822$ m.**

## Check yourself

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

1. If the tape is 2 cm too long, the measured readings are
   A. too small, so multiply by 30.02/30
   B. too large
   C. correct
   D. divide by 30.02
   Answer: A. Long tape under-reads. (Key point: Tape too long)

2. Horizontal distance is
   A. l' - h
   B. sqrt(l'^2 - h^2)
   C. l' cos h
   D. l' + h
   Answer: B. Pythagoras. (Key point: Horizontal)

3. Corrections applied
   A. slope first
   B. only slope
   C. tape length first then slope
   D. only length
   Answer: C. As in the table. (Key point: Order)

4. True total is
   A. greater
   B. 126.80
   C. same
   D. 125.822 m, less than measured 126.80
   Answer: D. Slope reduces more. (Key point: Result)

## Related in Surveying I

- [Correct horizontal distance, 28.00 m measured](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-fully-support-28-00m) — Surveying I, chapter 2
- [Horizontal length of 16 m, 29.8850 m tape](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-29-8850-16m-fully-supported) — Surveying I, chapter 2
- [Horizontal length of 30 m span, 50 m tape](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-50m-span-30m-26c) — Surveying I, chapter 2
- [True length of 1020 m line, 20 m tape](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-20m-1020m-line) — Surveying I, chapter 2, asked 2×
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