---
title: "Bedrock attitude: A 700 m N23E, C S71W"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:bh-hydropower-a700-n23e"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/bh-hydropower-a700-n23e
site: BCT Engineering
---

# Bedrock attitude: A 700 m N23E, C S71W

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

- Asked in: 2071 Magh, 5 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-hydropower-a700-n23e
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

Three boreholes A, B and C were drilled at featureless terrain for a hydropower project. Borehole A lies at 700 m due N23°E from borehole B and borehole C lies S71°W from borehole B [distance not printed]. The top of the bedrock has been encountered at the following depths of the three boreholes respectively. Find the attitude of the bedrock and the true thickness of the bed.
| Bore hole | Depth (bottom) m | Depth (top) m |
|---|---|---|
| A | -280 | -240 |
| B | -320 | -280 |
| C | -340 | -300 |

## Short answer

Using three-point method on top-of-bedrock depths (-240, -280, -300 m) with coordinates (assuming borehole C at 500 m S71°W of B), attitude is strike N64.6°W, dip 3.3° towards SSW (205°), true thickness = 40 m × cos(3.27°) = 39.9 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.

#### Reading the data
The table headings are interchanged: the top is the shallower level (A = -240, B = -280, C = -300 m) and the bottom is deeper (-280, -320, -340 m). The bed is 40 m thick in every hole, so $t_v = 40$ m. The distance BC is not printed; **BC = 500 m is assumed** (the method is the same for any value).

#### Coordinates (B at origin)
$$
\begin{aligned}
A &: x = 700\sin 23^\circ = 273.51\ \text{m},\ y = 700\cos 23^\circ = 644.35\ \text{m} \\
C &: x = 500\sin 251^\circ = -472.76\ \text{m},\ y = 500\cos 251^\circ = -162.78\ \text{m}
\end{aligned}
$$

#### Plane of the top of bedrock
$z = -280 + a x + b y$:
$$
\begin{aligned}
-240 &= -280 + 273.51a + 644.35b \\
-300 &= -280 - 472.76a - 162.78b
\end{aligned}
$$
Solving: $a = 0.0245$, $b = 0.0517$.

#### Dip, dip direction and strike
$$
\tan\delta = \sqrt{a^2+b^2} = 0.0572 \Rightarrow \delta = 3.27^\circ
$$
The bed descends toward the direction $\arctan(-a/-b)$ = **205.4°** (SSW), so the strike is $\ 205.4^\circ - 90^\circ = 115.4^\circ$, i.e. **N64.6°W**.

#### True thickness
All three boreholes show the same vertical thickness, 40 m, so
$$
t = t_v\cos\delta = 40\cos 3.27^\circ = 39.93\ \text{m}
$$

**Answer (with BC = 500 m): bedrock attitude = strike N64.6°W, dip 3.3° towards SSW (dip direction 205°); true thickness = 39.9 m.** The bed is nearly flat, so the true thickness is almost equal to 40 m.

## Check yourself

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

1. In the three-borehole method, why can the bedrock level be written as z = z0 + a x + b y?
   A. Because every bed is exactly horizontal
   B. Because a bed is a plane, so its level changes uniformly with position
   C. Because the boreholes lie on a straight line
   D. Because the level depends only on the distance from BH#1
   Answer: B. A bed is treated as a plane, so level varies linearly with east and north coordinates; the three borehole levels fix a and b. (Key point: Bed as a plane)

2. How does the solution interpret the table of depths?
   A. The bottom is shallower, so the bed is -40 m thick
   B. Only borehole A gives a valid thickness
   C. The thickness varies from 40 m to 60 m among holes
   D. The headings are interchanged: the shallower values are the top, and the bed is 40 m thick in every hole
   Answer: D. Top levels are -240, -280, -300 and bottoms are 40 m deeper in each hole, so tv = 40 m. (Key point: Interpreting the table)

3. The distance BC was not printed. How does the solution handle this?
   A. It says the attitude cannot be found without BC
   B. It assumes BC = 500 m, noting the method is the same for any value
   C. It takes BC equal to AB = 700 m by geometry
   D. It ignores borehole C and uses only A and B
   Answer: B. A value of 500 m is assumed to complete the coordinates; the method itself is unchanged. (Key point: Missing distance)

4. Since the bed dips only 3.27°, what is the true thickness?
   A. About 40 sin 3.27° = 2.3 m
   B. About 40 / cos 3.27° = 40.1 m
   C. About 20 m
   D. About 39.9 m, nearly equal to 40 m
   Answer: D. t = 40 cos 3.27° = 39.93 m; a gentle dip makes true and vertical thickness almost equal. (Key point: True thickness)

## Related in Engineering Geology II

- [Sandstone attitude: A N45W 900 m, C S20E 700 m](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-sandstone-a-n45w-c-s20e) — Engineering Geology II, chapter 6
- [Tunnel alignment from three boreholes](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Atunnel-alignment-three-boreholes) — Engineering Geology II, chapter 6
- [Borehole attitude: square 360 m, M N O P](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-attitude-square-360-mnop) — Engineering Geology II, chapter 6
- [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×
- [Depth at fourth borehole P (coal seam)](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-depth-at-p-coal-seam) — Engineering Geology II, chapter 6
- [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×

## Related in other subjects

- [Bore hole altitude of fractured bedrock](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Abore-hole-altitude-of-fractured) — Engineering Geology I, chapter 5
- [Managing three hydropower project risks](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Arisk-manage-three-hydropower-risks) — Project Engineering, chapter 5