---
title: "Three-point problem: A 600 m N, C 300 m E (500, 100, 400)"
subject: "Engineering Geology I"
chapter: 5
key: "semester_3/engineering_geology_i:threepoint-problem-a-600-m-2"
source: https://www.bctengineer.com/q/semester_3/engineering_geology_i/threepoint-problem-a-600-m-2
site: BCT Engineering
---

# Three-point problem: A 600 m N, C 300 m E (500, 100, 400)

Engineering Geology I · Chapter 5: Structural Geology

- Asked in: 2061 Baisakh (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-2
- 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, 100 m and 400 m respectively. Find the attitudes (strike, dip direction and dip amount) of the bed rock whose bedding plane is passing through these points.

## Short answer

Locate a point D on AB at elevation 400 m (450 m north of B). The line between D and C is a strike line, running N33.7°W. The plane dips S56.3°W at 50.2°.

## 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 100 m.

```text
        A (500 m)
        |
        | 600 m
        |
        B (100 m) -------- C (400 m)   [300 m east]
```

#### Step 1: Strike line
Along AB the altitude rises uniformly from 100 m (B) to 500 m (A), i.e. 400 m in 600 m (0.6667 m per m).
The point D on AB with altitude 400 m (equal to C) is at a distance from B of

$$
BD = \frac{400-100}{500-100} \times 600 = 450\ \text{m north of B}
$$

Line DC joins two points at 400 m, so it is the strike line. It runs from D (0, 450) to C (300, 0).

#### Step 2: Strike direction
Taking east as +x and north as +y, the northward rise is $b = (500-100)/600 = 0.6667$ and the eastward rise is $a = (400-100)/300 = 1.0$.

From D to C the line runs 300 m east and 450 m south. The acute angle it makes with the north-south line is

$$
\theta = \arctan\left(\frac{300}{450}\right) = 33.69°
$$

D to C runs towards S33.7°E, so the strike is **N33.7°W** (the same line as S33.7°E).

Cross-check: the strike line is perpendicular to the direction of rise (a, b) = (1.0, 0.6667), which points to N56.3°E, giving a strike azimuth of 146.31° (or 326.31°).

#### Step 3: Dip direction and dip amount
The bed rises towards the north-east (A and C are higher than B), so it dips the opposite way (down the slope), at 90° to the strike. Dip direction azimuth = 236.31°, which is **S56.3°W**.

$$
\tan\delta = \sqrt{a^2 + b^2} = \sqrt{1.0^2 + 0.6667^2} = 1.2019 \Rightarrow \delta = 50.24°
$$

**Answer: Strike N33.7°W; dip direction S56.3°W; dip amount 50.2°.**

## 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 at 600 m north of B 100 m; C 400 m, 300 m east of B)?
   A. N33.7°E
   B. N33.7°W
   C. N56.3°W
   D. E-W
   Answer: B. Strike is perpendicular to the slope gradient (a, b). (Key point: Strike result)

3. The dip direction is
   A. S56.3°E
   B. N56.3°W
   C. S56.3°W
   D. S33.7°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. 33.7°
   B. 56.3°
   C. 39.8°
   D. 50.2°
   Answer: D. a and b are the eastward and northward rises. (Key point: Dip amount)

## Close variants set in other exams

- [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×
- [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×

## Related in Engineering Geology I

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