---
title: "Three-point problem: A 800 m N, C 400 m W (500, 100, 300)"
subject: "Engineering Geology I"
chapter: 5
key: "semester_3/engineering_geology_i:threepoint-problem-a-800-m-n"
source: https://www.bctengineer.com/q/semester_3/engineering_geology_i/threepoint-problem-a-800-m-n
site: BCT Engineering
---

# Three-point problem: A 800 m N, C 400 m W (500, 100, 300)

Engineering Geology I · Chapter 5: Structural Geology

- Asked in: 2062 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-800-m-n
- Whole chapter: https://www.bctengineer.com/md/semester_3/engineering_geology_i/chapter-5

## Question

Point A is 800 m N of Point B and Point C is 400 m west of Point B. The altitudes of A, B and C are 500 m, 100 m and 300 m respectively. Find the attitudes (strike, dip direction and dip amount) of the bed rock whose bedding plane passes through these points.

## Short answer

Strike N45°E, dip direction S45°E, dip amount 35.3°.

## 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 800 m north of B (altitude 500 m). C is 400 m west of B (altitude 300 m). B is at 100 m.

```text
        A (500 m)
        |
        | 800 m
        |
  C (300 m) -------- B (100 m)   [C is 400 m west]
```

#### Step 1: Strike line
Along AB the altitude rises uniformly from 100 m (B) to 500 m (A), i.e. 400 m in 800 m (0.5 m per m).
The point D on AB with altitude 300 m (equal to C) is at a distance from B of

$$
BD = \frac{300-100}{500-100} \times 800 = 400\ \text{m north of B}
$$

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

#### Step 2: Strike direction
Taking east as +x and north as +y, the northward rise is $b = (500-100)/800 = 0.5$ and the eastward rise is $a = (300-100)/(-400) = -0.5$ (the bed rises towards the west).

From D to C the line runs 400 m west and 400 m south. The acute angle it makes with the north-south line is

$$
\theta = \arctan\left(\frac{400}{400}\right) = 45°
$$

D to C runs towards S45°W, so the strike is **N45°E** (the same line as S45°W).

Cross-check: the strike line is perpendicular to the direction of rise (a, b) = (−0.5, 0.5), which points to N45°W, giving a strike azimuth of 45° (or 225°).

#### Step 3: Dip direction and dip amount
The bed rises towards the north-west (A and C are higher than B), so it dips the opposite way (down the slope), at 90° to the strike. Dip direction azimuth = 135°, which is **S45°E**.

$$
\tan\delta = \sqrt{a^2 + b^2} = \sqrt{0.5^2 + 0.5^2} = 0.7071 \Rightarrow \delta = 35.26°
$$

**Answer: Strike N45°E; dip direction S45°E; dip amount 35.3°.**

## 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. Join A to C directly
   B. Join the highest and lowest points
   C. Draw a line perpendicular to AB
   D. Find a point on AB with the same altitude as C and join it to C
   Answer: D. 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 800 m north of B 100 m; C 300 m, 400 m west of B)?
   A. N45°E
   B. N45°W
   C. E-W
   D. N-S
   Answer: A. Strike is perpendicular to the slope gradient (a, b). (Key point: Strike result)

3. The dip direction is
   A. S45°W
   B. S45°E
   C. due north
   D. N45°W
   Answer: B. 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. 45°
   B. 26.6°
   C. 35.3°
   D. 14.0°
   Answer: C. a and b are the eastward and northward rises. (Key point: Dip amount)

## Close variants set in other exams

- [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 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 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×

## 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
- [Dip direction from strike N55°E, dip 30°](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Adip-direction-from-strike-n55e) — Engineering Geology I, chapter 5
- [Strike of limestone bed, dip N40°W, 64°](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-limestone-bed-dip) — Engineering Geology I, chapter 5
- [Strike when dip direction is N40°W](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-when-dip-direction-is) — Engineering Geology I, chapter 5
- [Dip amount, strike; fold identification criteria](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Adip-amount-strike-fold-identification) — Engineering Geology I, chapter 5