---
title: "True thickness from apparent thickness 210 m"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:bh-quartzite-thickness-210-attitude"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/bh-quartzite-thickness-210-attitude
site: BCT Engineering
---

# True thickness from apparent thickness 210 m

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

- Asked in: 2072 Asoj, 4 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/bh-quartzite-thickness-210-attitude
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

Three bore holes were drilled to find out a stable place for dam foundation of a hydroelectric project. The apparent thickness of quartzite was found as 210 m. The attitude of the quartzite bed was 220°/36° NE. Calculate the true thickness of bedrock.

## Short answer

True thickness equals vertical thickness times cosine of dip: 210 m × cos(36°) = 169.9 m.

## Answer

**Principle:** in a vertical borehole the thickness measured is the **vertical (apparent) thickness** $t_v$. The true thickness (perpendicular to the bedding) is smaller for a dipping bed:
$$
t = t_v\cos\delta
$$

#### Given
$t_v = 210$ m, dip $\delta = 36^\circ$ (attitude 220°/36° NE).

#### Calculation
$$
\begin{aligned}
t &= 210\cos 36^\circ \\
&= 210 \times 0.8090 \\
&= 169.89\ \text{m}
\end{aligned}
$$

```text
        borehole
          |
     _____|______  top of bed
    |     | tv   /
    |     |    /  t (true)
    |_____|__/__  bottom of bed
          |/ dip 36 deg
```

**Answer: true thickness of the quartzite = 169.9 m.**

## Check yourself

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

1. What does a vertical borehole measure in a dipping bed?
   A. The true thickness, perpendicular to bedding
   B. Vertical (apparent) thickness, which is larger than the true thickness
   C. The strike length of the bed
   D. The thickness along the dip direction only
   Answer: B. A vertical hole cuts the bed obliquely, so the measured thickness exceeds the thickness perpendicular to bedding. (Key point: Apparent vs true thickness)

2. Which formula gives true thickness from vertical thickness?
   A. t = tv sin(dip)
   B. t = tv / cos(dip)
   C. t = tv tan(dip)
   D. t = tv cos(dip)
   Answer: D. True thickness is the component of the vertical thickness normal to the bedding: tv cos(dip). (Key point: Formula)

3. With tv = 210 m and dip 36°, what is the true thickness?
   A. About 123.4 m
   B. About 169.9 m
   C. About 259.6 m
   D. About 210 m, since dip direction is NE
   Answer: B. 210 x cos 36° = 210 x 0.809 = 169.9 m; sin would give 123.4 m. (Key point: Result)

## Related in Engineering Geology II

- [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×
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## Related in other subjects

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- [Stresses in gravity dam with drain holes](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-stresses-figure) — Hydro Power, chapter 4
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- [True length: tape found 2.5 cm too long](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-825-plus-750-m) — Surveying I, chapter 2