---
title: "Three-point problem: A 600 m N, C 300 m E (500, 400, 400)"
subject: "Engineering Geology I"
chapter: 5
key: "semester_3/engineering_geology_i:threepoint-problem-a-600-m"
source: https://www.bctengineer.com/q/semester_3/engineering_geology_i/threepoint-problem-a-600-m
site: BCT Engineering
---

# Three-point problem: A 600 m N, C 300 m E (500, 400, 400)

Engineering Geology I · Chapter 5: Structural Geology

- Asked in: 2065 Shrawan (old course), 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/engineering_geology_i/threepoint-problem-a-600-m
- Whole chapter: https://www.bctengineer.com/md/semester_3/engineering_geology_i/chapter-5

## Question

Point A is 600 m North of point B and point C is 300 m East of point B. The altitudes of A, B and C are 500 m, 400 m and 400 m respectively. Find the attitude of the bed rock, the bedding plane of which is passing through these points.

## Short answer

Strike is E-W (N90°E), dip direction due south, dip amount 9.5°.

## Answer

**Method**: the three-point problem. Three points at known altitudes define a plane. Find a point on the line AB with the same altitude as C; the line joining it to C is a **strike line** (a horizontal line on the bed).

**Given**: B is the origin. A is 600 m north of B (altitude 500 m). C is 300 m east of B (altitude 400 m). B is at 400 m.

```text
        A (500 m)
        |
        | 600 m
        |
        B (400 m) -------- C (400 m)   [300 m east]
```

#### Step 1: Strike line
Along AB the altitude rises uniformly from 400 m (B) to 500 m (A), i.e. 100 m in 600 m (0.1667 m per m).
The point D on AB with altitude 400 m (equal to C) is at a distance from B of

$$
BD = \frac{400-400}{500-400} \times 600 = 0\ \text{m}
$$

So D coincides with B, and line BC, which joins two points at 400 m, is itself the strike line.

#### Step 2: Strike direction
BC runs due east, so the strike is **E-W (N90°E)**.

Cross-check: taking east as +x and north as +y, the eastward rise is $a = (400-400)/300 = 0$ and the northward rise is $b = (500-400)/600 = 0.1667$. The strike line is perpendicular to the direction of rise (due north), giving an azimuth of 90°.

#### Step 3: Dip direction and dip amount
The bed rises towards A (north), so it dips the opposite way (down the slope), at 90° to the strike. Dip direction azimuth = 180°, which is **due south**.

$$
\tan\delta = \sqrt{a^2 + b^2} = \sqrt{0^2 + 0.1667^2} = 0.1667 \Rightarrow \delta = 9.46°
$$

**Answer: Strike E-W (N90°E); dip direction due south; dip amount 9.5°.**

## Check yourself

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

1. How is the strike line found in a three-point problem?
   A. Find a point on AB with the same altitude as C and join it to C
   B. Join A to C directly
   C. Join the highest and lowest points
   D. Draw a line perpendicular to AB
   Answer: A. Two points of equal altitude lie on a horizontal line of the bed, which is the strike line. (Key point: Strike line method)

2. What is the strike of the bed (A 500 m, 600 m north of B 400 m; C 400 m, 300 m east of B)?
   A. N-S
   B. E-W (N90°E)
   C. N45°E
   D. N45°W
   Answer: B. Strike is perpendicular to the slope gradient (a, b). (Key point: Strike result)

3. The dip direction is
   A. due north
   B. due east
   C. due south
   D. S45°W
   Answer: C. The bed dips down the slope, at 90° to the strike. (Key point: Dip direction)

4. The dip amount is found from tan(dip) = sqrt(a^2 + b^2) and equals
   A. 16.7°
   B. 45°
   C. 5.0°
   D. 9.5°
   Answer: D. a and b are the eastward and northward rises. (Key point: Dip amount)

## Related in Engineering Geology I

- [Three-point problem: A 600 m N, C 300 m E (500, 100, 400)](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Athreepoint-problem-a-600-m-2) — Engineering Geology I, chapter 5, asked 4×
- [Three-point problem: A 600 m N, C 400 m W (400, 100, 300)](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Athreepoint-problem-a-600-m-n) — Engineering Geology I, chapter 5, asked 4×
- [Three-point problem: A 800 m N, C 400 m W (500, 100, 300)](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Athreepoint-problem-a-800-m-n) — Engineering Geology I, chapter 5, asked 4×
- [Three-point problem: A 800 m N, C 600 m E (600, 200, 500)](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Athreepoint-problem-a-800-m) — Engineering Geology I, chapter 5, asked 4×

## Related in other subjects

- [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×