Bearings (Edexcel GCSE Maths): Revision Notes
Bearings
What are bearings?
Bearings are a way of describing direction using angles. They tell us exactly which way to travel from one point to reach another point.
Bearings are a fundamental concept in navigation and geometry, providing a precise method for indicating direction. Understanding how to work with bearings is essential for solving many geometric problems and real-world navigation tasks.
The Two Fundamental Rules of Bearings:
- Bearings are always measured clockwise from north
- Bearings are always written as three-figure numbers
These rules must be followed in every bearing calculation!
If the angle is less than 100°, you need to add zeros at the beginning to make it three figures. For example, if the angle is 48°, you write the bearing as 048°.
How to measure bearings
To find a bearing, you need to follow a systematic approach that ensures accuracy and consistency.
- Start by drawing a line pointing north from your starting point
- Measure the angle clockwise from north to your destination
- Write your answer using three figures
Always remember that the measurement starts from north and goes in the clockwise direction. This is different from how we might naturally think about angles in mathematics, where we often measure counterclockwise from the positive x-axis.
For example, if you measure an angle of 109° clockwise from north, the bearing is 109°.
Reverse bearings
Sometimes you need to find the bearing for the return journey. This is called a reverse bearing and represents the direction you would travel to get back to your starting point.
Rules for Calculating Reverse Bearings:
- Add 180° to the original bearing if the result is less than 360°
- Subtract 180° from the original bearing if adding 180° gives you more than 360°
The key is to ensure your final answer stays within the range 000° to 359°.
Worked Examples: Reverse Bearings
Example 1: If the bearing from A to B is 048°, then the bearing from B to A is: 048° + 180° = 228°
Example 2: If the bearing from A to B is 251°, then the bearing from B to A is: 251° - 180° = 071° (We subtract because 251° + 180° = 431°, which is greater than 360°)
Compass points
You should know the main compass directions and their corresponding bearings. These reference points are crucial for understanding and checking your work.
| Direction | Bearing |
|---|---|
| North (N) | 000° |
| North-East (NE) | 045° |
| East (E) | 090° |
| South-East (SE) | 135° |
| South (S) | 180° |
| South-West (SW) | 225° |
| West (W) | 270° |
| North-West (NW) | 315° |
The angle between north and east is 90°, and the angle between north and north-east is 45°. These quarter and eighth divisions of the compass are particularly useful for quick mental checks of your calculations.
Worked example
Let's examine a comprehensive step-by-step example to see how bearings work in practice.
Worked Example: Combined Bearings
Problem: Jake walks from point O to point A. The bearing is 125°. Then he walks from A to B, where the bearing is 100°. What is the total bearing from O to B?
Solution: Step 1: Identify the given information
- First bearing (O to A): 125°
- Second bearing (A to B): 100°
Step 2: Calculate the total bearing Total bearing = 125° + 100° = 225°
Note: This problem can also be solved by analysing the angles in a diagram and adding them systematically, which often provides a good way to double-check your answer.
Exam tips
Here are some essential strategies to help you succeed with bearing problems in exams and assessments.
Key Exam Tips:
- Always check your bearing is written with three figures
- Remember that bearings are measured clockwise from north, not from any other direction
- When finding reverse bearings, decide whether to add or subtract 180° by checking if your answer will be more or less than 360°
- Draw clear diagrams with north arrows to help you visualise the problem
- Double-check your arithmetic, especially when adding or subtracting 180°
Summary
Key Points to Remember:
- Bearings are always measured clockwise from north
- All bearings must be written as three-figure numbers (add zeros if needed)
- Reverse bearings: add or subtract 180° depending on the size of the angle
- Know your compass points - North = 000°, East = 090°, South = 180°, West = 270°
- Always draw north arrows on your diagrams to help you work out the correct angles