---
title: "Rock layer attitude: A 900 m N, C 800 m W"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:bh-rock-layer-a900n-c800w"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/bh-rock-layer-a900n-c800w
site: BCT Engineering
---

# Rock layer attitude: A 900 m N, C 800 m W

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

- Asked in: 2077 Chaitra, 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-a900n-c800w
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

Bore hole A is 900 m due north of Bore hole B and Bore hole C is 800 m due west of bore hole B. The top and bottom of a rock layer are reached at the following altitudes relative to the sea level in the three holes.
Bore Hole A: -350 m and -410 m
Bore Hole B: -310 m and -370 m
Bore Hole C: -390 m and -450 m
Find the attitude and true thickness of the rock layer.

## Short answer

Three-point plane solution gives top-surface gradients 0.1000 m/m east and -0.0444 m/m north. Attitude is strike N24.0°E, dip 6.2° toward WNW (294°); true thickness = 59.6 m from 60 m vertical thickness.

## 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, x east, y north)
A = (0, 900), C = (-800, 0), B = (0, 0). Levels of the top: A = -350 m, B = -310 m, C = -390 m. The layer is 60 m thick in each hole (-350 to -410, -310 to -370, -390 to -450), so $t_v = 60$ m.

#### Gradients of the top surface
$$
\begin{aligned}
b &= \frac{z_A - z_B}{900} = \frac{-350 - (-310)}{900} = -0.0444 \\
a &= \frac{z_B - z_C}{800} = \frac{-310 - (-390)}{800} = 0.1000
\end{aligned}
$$
The level falls northward and rises eastward, so the bed descends towards the NW/WNW.

#### Dip, dip direction and strike
$$
\tan\delta = \sqrt{a^2+b^2} = 0.1094 \Rightarrow \delta = 6.25^\circ
$$
The bed descends toward the direction $\arctan(-a/-b)$ = **294.0°** (WNW), so the strike is $\ 294.0^\circ - 90^\circ = 204.0^\circ$, i.e. **N24.0°E**.

#### True thickness
All three boreholes show the same vertical thickness, 60 m, so
$$
t = t_v\cos\delta = 60\cos 6.25^\circ = 59.64\ \text{m}
$$

**Answer: attitude of the layer = strike N24.0°E, dip 6.2° towards WNW (dip direction 294°); true thickness = 59.6 m.**

## Check yourself

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

1. How are the gradients a and b calculated?
   A. From thickness
   B. From sea level
   C. From 900 + 800
   D. From level differences over distance: a = 80/800, b = −40/900
   Answer: D. Use the top surface levels. (Key point: Gradient method)

2. What is the dip?
   A. 6.25°, from tan = sqrt(a² + b²) = 0.1094
   B. 0.1094°
   C. 10°
   D. 60°
   Answer: A. Resultant gradient gives tan(dip). (Key point: Dip)

3. How is true thickness found from vertical thickness 60 m?
   A. t = tv/cos
   B. t = tv cos(dip) = 59.6 m
   C. t = tv sin(dip)
   D. 60 m exactly
   Answer: B. True thickness is perpendicular to bedding, so vertical thickness is multiplied by cos(dip). (Key point: True thickness)

4. Which way does the bed descend?
   A. SE
   B. NE
   C. WNW (294°), as level falls northward and rises eastward
   D. E
   Answer: C. Level falls toward north and west, so it descends towards WNW. (Key point: Direction)

## Close variants set in other exams

- [Rock layer attitude: A 700 m N, C 600 m W](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-rock-layer-a700n-c600w) — Engineering Geology II, chapter 6, asked 2×

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