---
title: "Rock layer attitude: A 700 m N, C 600 m W"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:bh-rock-layer-a700n-c600w"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/bh-rock-layer-a700n-c600w
site: BCT Engineering
---

# Rock layer attitude: A 700 m N, C 600 m W

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

- Asked in: 2068 Bhadra, 6 marks
- 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-rock-layer-a700n-c600w
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

Bore hole A is 700 m due north of bore hole B and bore hole C is 600 m due west of bore hole B. The tops and bottoms of a rock layer are reached at the following altitudes relative to the sea level in three holes.
Bore hole A: -410 m and -430 m
Bore hole B: -380 m and -400 m
Bore hole C: -430 m and -450 m
Find the attitude and thickness of the rock layer.

## Short answer

Three-point method using top depths (-410, -380, -430 m) for boreholes A (0,700), B (0,0), C (-600,0) yields strike N27.2°E, dip 5.4° towards WNW (297°), true thickness = 20 m × cos(5.35°) = 19.9 m.

## Answer

A bed is a plane, so its level changes uniformly in plan: $z = z_B + a x + b y$, where $a$ and $b$ are the rates of change of level per metre east and north. This is the analytical form of the three-point (strike-line) method.

#### Data and coordinates (B at origin)
A = (0, 700), C = (-600, 0). Levels of the top: A = -410 m, B = -380 m, C = -430 m. The layer is 20 m thick in each hole (-410/-430, -380/-400, -430/-450), so $t_v = 20$ m.

#### Gradients of the top surface
$$
\begin{aligned}
b &= \frac{-410 - (-380)}{700} = -0.0429 \\
a &= \frac{-380 - (-430)}{600} = 0.0833
\end{aligned}
$$
The level falls northward and rises eastward, so the layer dips towards the NW.

#### Dip, dip direction and strike
$$
\tan\delta = \sqrt{a^2+b^2} = 0.0937 \Rightarrow \delta = 5.35^\circ
$$
The bed descends toward the direction $\arctan(-a/-b)$ = **297.2°** (WNW), so the strike is $\ 297.2^\circ - 90^\circ = 207.2^\circ$, i.e. **N27.2°E**.

#### True thickness
All three boreholes show the same vertical thickness, 20 m, so
$$
t = t_v\cos\delta = 20\cos 5.35^\circ = 19.91\ \text{m}
$$

**Answer: attitude of the layer = strike N27.2°E, dip 5.4° towards WNW (dip direction 297°); true thickness = 19.9 m.**

## Check yourself

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

1. Taking B as origin, where do A and C plot?
   A. A = (700, 0) and C = (0, 600)
   B. A = (0, -700) and C = (600, 0)
   C. A = (0, 700) and C = (600, 0)
   D. A = (0, 700) and C = (-600, 0)
   Answer: D. A is due north (positive y) and C is due west (negative x). (Key point: Coordinates)

2. Which gradients result?
   A. b = +0.0429, a = -0.0833
   B. b = -0.0429 (falls northward), a = +0.0833 (rises eastward)
   C. b = -0.0833, a = +0.0429
   D. b = -0.0429, a = -0.0833
   Answer: B. Level at A is 30 m lower than B over 700 m north; B is 50 m higher than C over 600 m east. (Key point: Gradients)

3. What attitude is found?
   A. Strike N27.2°W, dip 5.4° towards ENE
   B. Strike N62.8°W, dip 5.4° towards WNW
   C. Strike N27.2°E, dip 9.4° towards ESE
   D. Strike N27.2°E, dip 5.4° towards WNW (297°)
   Answer: D. tan(dip)=0.0937 gives 5.35°; descent direction 297.2°; strike 90° off it, N27.2°E. (Key point: Attitude)

4. What is the layer's true thickness?
   A. About 1.9 m from 20 sin 5.35°
   B. About 19.9 m from 20 cos 5.35°
   C. About 20.1 m from 20 / cos 5.35°
   D. About 40 m
   Answer: B. Vertical thickness is 20 m in every hole, so t = 20 x 0.9956 = 19.91 m. (Key point: True thickness)

## Close variants set in other exams

- [Rock layer attitude: A 900 m N, C 800 m W](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-rock-layer-a900n-c800w) — Engineering Geology II, chapter 6, asked 2×

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