Bearings
Bearings are used to describe direction. In GCSE Maths, bearings are measured clockwise from north and written as three-figure angles.
Bearings are measured:
• from north
• clockwise
• using three figures
How to measure a bearing
Start from the north line, then measure clockwise until you reach the direction line.
Example 1: Measuring a bearing
A ship travels east from a port.
East is 90° clockwise from north.
Bearing = 090°
Example 2: Another bearing
A plane travels south-east.
South-east is halfway between east (090°) and south (180°).
Bearing = 135°
Writing bearings correctly
Bearings must always have three digits.
Correct: 045°
Incorrect: 45°
Reverse bearings
A reverse bearing is the direction going back the opposite way.
If the bearing is less than 180°, add 180°.
If the bearing is 180° or more, subtract 180°.
Example 3: Find a reverse bearing
A boat travels from A to B on a bearing of 070°.
To find the reverse bearing from B to A:
070° + 180° = 250°
The reverse bearing is 250°.
Example 4: Another reverse bearing
A helicopter travels on a bearing of 230°.
Since 230° is greater than 180°, subtract 180°:
230° − 180° = 050°
Bearings in scale drawing questions
Bearings are often combined with distances and scale drawings in GCSE exam questions.
Example 5: Using a scale drawing
A town is 6 cm from another town on a map with scale 1 cm = 5 km.
The real distance is:
6 × 5 = 30 km
A very common mistake is measuring anti-clockwise instead of clockwise. Always start from north and move clockwise.
Draw a north line whenever you solve a bearings question. This helps avoid direction mistakes and makes your working clearer.
Video explanation
A short Worthing Maths Tutor video explanation for bearings can be embedded here later to improve student engagement and time on page.
Practice questions
- Write east as a bearing.
- Write north-west as a bearing.
- Find the reverse bearing of 120°.
- Find the reverse bearing of 315°.
- A ship travels 8 cm on a map where 1 cm = 12 km. Find the real distance.
Answers
- 090°
- 315°
- 300°
- 135°
- 96 km
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