GCSE Maths Bearings Notes
A bearing is an angle measured clockwise from north, always written with three figures. Bearings link angle rules with trigonometry.
Key concepts
- Three-figure bearing
- Always use three digits, measured clockwise from north, e.g. 072° not 72°.
- Measured from north
- Draw a north line at the point you are measuring from and turn clockwise to the target.
- Back bearing
- The bearing of the return journey — add or subtract 180°.
Key formulas
Back bearing
add 180° if original < 180°, otherwise subtract 180°
Worked example
The bearing of B from A is 040°. Find the bearing of A from B.
- 1The original bearing is less than 180°, so add 180°.
- 2040° + 180° = 220°.
- 3Write it as a three-figure bearing.
Answer: 220°
Common mistakes
✗ Writing a bearing with only two figures, e.g. 65°.
✓ Pad with a leading zero: 065°.
✗ Measuring anticlockwise or from the wrong point.
✓ Always measure clockwise from north at the point named after 'from'.
✗ Adding 180° when you should subtract for a back bearing.
✓ If the bearing is 180° or more, subtract 180° instead of adding.
Quick check
Try these, then reveal the answers.
Write 8° as a three-figure bearing.Reveal answer
008°
Back bearing of 300°?Reveal answer
120°
A bearing due east is?Reveal answer
090°
Exam tips
- Draw and label the north line at each point before measuring or calculating.
- Use alternate and co-interior angles between parallel north lines to find missing bearings.
- For distance problems, combine bearings with the sine or cosine rule.
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Frequently asked questions
Why are bearings written with three figures?+
Three figures avoid ambiguity and keep bearings consistent, so 5° is always written 005°.
How do bearings connect to trigonometry?+
Bearing diagrams often form triangles, so you use SOH CAH TOA or the sine and cosine rules to find distances and angles.
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