Bearings are angles used to describe the direction from one place to another. They often appear in GCSE Maths questions involving maps, ships, aeroplanes and distances.
The good news is that bearings questions become much easier when you remember three simple rules.
1. The three rules of bearings
- Always measure from North. North is shown by an arrow pointing upwards on a standard diagram.
- Measure clockwise. Turn to the right from North until you reach the direction you want.
- Write three digits. For example, write $045^\circ$, not $45^\circ$, and $090^\circ$, not $90^\circ$.
2. Understanding bearings
Look at these four main directions.
The main compass directions and their bearings.
| Direction | Bearing |
|---|---|
| North | $000^\circ$ |
| East | $090^\circ$ |
| South | $180^\circ$ |
| West | $270^\circ$ |
Remember: bearings start at North and go clockwise.
For example, halfway between North and East is $045^\circ$.
Example 1: Finding a bearing
A ship sails from point A towards point B. The direction is shown below.
The bearing is measured clockwise from North at A.
Step 1: Start at North at point A.
Step 2: Turn clockwise towards B.
Step 3: Read the angle.
The answer is $\boxed{045^\circ}$.
Example 2: Finding the missing angle
A bearing is $125^\circ$. What is the angle between North and the direction of travel?
Bearings are measured clockwise from North, so the angle is simply:
$ \boxed{125^\circ} $
But what if you are given the smaller angle of \(35^\circ\) between North and a direction to the East?
You calculate:
$ 90^\circ+35^\circ=125^\circ $
The bearing is $\boxed{125^\circ}$.
Example 3: Finding the reverse bearing
A reverse bearing tells you the direction back to where you started.
For example, the bearing from A to B is $060^\circ$. Find the bearing from B to A.
To find the reverse bearing, add $180^\circ$:
$060^\circ+180^\circ=240^\circ $
Answer: \[\boxed{240^\circ}\]
Remember:
- If the bearing is less than $180^\circ$, add $180^\circ$.
- If the bearing is greater than $180^\circ$, subtract $180^\circ$.
The key facts to remember
- Start at North.
- Measure clockwise.
- Always write three digits.
- For reverse bearings, add or subtract $180^\circ$.
These are the essential skills to aim for on a GCSE bearings question.