---
title: "True thickness from vertical thickness 150 m"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:true-thickness-vertical-150-dip-47"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/true-thickness-vertical-150-dip-47
site: BCT Engineering
---

# True thickness from vertical thickness 150 m

Engineering Geology II · Chapter 6: Measurement, analysis and interpretation of structural geological data

- Asked in: 2076 Baisakh, 3 marks
- Video: [Help video for calculating true thickness](https://www.youtube.com/watch?v=bJSBg7VTzM4) — Catherine Mottram
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/true-thickness-vertical-150-dip-47
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

The vertical thickness of inclined bedrock limestone is 150 m and the true dip amount is 47°. Calculate the true thickness of the limestone bedrock.

## Short answer

True thickness equals vertical thickness times cosine of dip: 150 m × cos(47°) = 102.3 m.

## Answer

**Principle:** the vertical thickness $t_v$ is measured in a vertical hole; the true thickness $t$ is measured normal to the bedding. For a bed dipping at $\delta$:
$$
t = t_v\cos\delta
$$

```text
         |  tv
    _____|_____
    \    |    \     t = tv cos(dip)
     \___|_____\
          dip
```

#### Calculation
$$
\begin{aligned}
t &= 150\cos 47^\circ \\
&= 150 \times 0.6820 \\
&= 102.30\ \text{m}
\end{aligned}
$$

**Answer: true thickness of the limestone = 102.3 m.**

## Check yourself

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

1. Which relationship holds for a bed dipping at δ?
   A. True thickness = vertical thickness x cos δ
   B. True thickness = vertical thickness x sin δ
   C. True thickness = vertical thickness / cos δ
   D. True thickness = vertical thickness x tan δ
   Answer: A. True thickness is measured normal to bedding, which is the vertical component times cos δ. (Key point: Vertical vs true thickness)

2. What true thickness results for tv = 150 m and dip 47°?
   A. About 109.7 m
   B. About 219.9 m
   C. About 102.3 m
   D. About 150 m
   Answer: C. 150 x 0.6820 = 102.3 m; sin 47° would give 109.7 m. (Key point: Calculation)

3. Why is the true thickness less than the vertical thickness?
   A. The perpendicular distance between bedding surfaces is shorter than the vertical distance between them for a dipping bed
   B. Because the bed thins with depth
   C. Because the vertical hole misses part of the bed
   D. Because dip direction subtracts from thickness
   Answer: A. cos δ < 1 for any dip greater than 0°, so t < tv. (Key point: Relative size)

## Related in Engineering Geology II

- [True thickness: limestone vertical 600 m](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Atrue-thickness-limestone-600m) — Engineering Geology II, chapter 7
- [Limestone true thickness: A 600 m N28E, C 400 m S10W](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-limestone-true-thickness-a600) — Engineering Geology II, chapter 6, asked 2×
- [Limestone true thickness across stream](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Astream-limestone-true-thickness) — Engineering Geology II, chapter 6
- [Reserve: limestone dip 30, apparent 20 m](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Areserve-limestone-dip-30) — Engineering Geology II, chapter 7
- [True dip from two apparent dips](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Atrue-dip-from-apparent-dips) — Engineering Geology II, chapter 6
- [True thickness from apparent thickness 210 m](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-quartzite-thickness-210-attitude) — Engineering Geology II, chapter 6

## Related in other subjects

- [Strike of limestone bed, dip N40°W, 64°](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-limestone-bed-dip) — Engineering Geology I, chapter 5
- [Strike of limestone bedrock dipping N31°W](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-limestone-bedrock-dipping) — Engineering Geology I, chapter 5
- [Calculating apparent dip from true dip](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Acalculating-apparent-dip-from-true) — Engineering Geology I, chapter 5, asked 2×
- [Dip amount, strike; fold identification criteria](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Adip-amount-strike-fold-identification) — Engineering Geology I, chapter 5