GCSE MATHS • HIGHER TIER
Three-Figure Bearings Made Simple
Learn how to read, write and draw three-figure bearings, find reverse bearings and apply bearings to GCSE navigation and trigonometry problems.
Clear method
Exam practice
Worked proofs
Three-Figure Bearings in Four Moves
1
Start at North
Every bearing begins from a North line at the starting point.
2
Measure Clockwise
Measure the angle clockwise from North to the required direction.
3
Use Three Figures
Write every bearing using three digits, adding a leading zero when necessary.
4
Check the Direction
Make sure the angle and direction match the diagram before giving your final answer.
What You’ll Learn
Understand Bearings
Understand that a bearing describes direction using an angle measured clockwise from North.
Write Three-Figure Bearings
Write bearings using three digits, such as 045°, 090°, 180° and 315°.
Draw Bearings Accurately
Use a North line and protractor to construct bearings accurately.
Find Reverse Bearings
Calculate the direction back to a starting point using the reverse bearing rule.
Connect Bearings with Trigonometry
Recognise how Higher Tier bearing questions can combine with Pythagoras, SOHCAHTOA, the Sine Rule and the Cosine Rule.
Key Rules
Measure clockwise
Bearings are always measured clockwise.
Measure from North
Every bearing starts from the North line.
Use three figures
Write bearings with three digits, even when the angle is below 100°.
Use a degree sign
Bearings are angles and should include °.
- Examples: 045° 090° 180° 315°
Worked Proof: Main Compass Direction
Question: What is the bearing of East?
1. Start at North
Begin from the North line.
2. Measure Clockwise
Turn clockwise from North to East.
3. Write Three Figures
The angle is 90°, so write it as 090°.
4. Answer
090°
More Worked Examples
1
Bearing of South
Question: What is the bearing of South?
North to South is half a turn.
2
Bearing of West
Question: What is the bearing of West?
North to West clockwise is 270°.
3
Angle Less Than 100°
Question: A direction is 45° clockwise from North. Write the bearing.
Use a leading zero because the angle is less than 100°.
4
Three-Figure Angle
Question: A direction is 120° clockwise from North. Write the bearing.
The angle is already written using three figures.
- Common GCSE Mistakes
- Measuring anti-clockwise instead of clockwise.
- Measuring from a line other than North.
- Writing fewer than three figures.
- Using the wrong reverse bearing.
- Misreading the protractor scale.
- Exam Tips
- Draw or identify the North line first.
- Measure clockwise from North every time.
- Add a leading zero to bearings below 100°.
- Use ±180° carefully for reverse bearings.
- Check your protractor scale before reading the angle.
Topics to Revise Next
Basic Pythagoras
3D Pythagoras
SOHCAHTOA
Sine Rule
Cosine Rule
Scale Drawings
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Three-Figure Bearings Tutorial
Step-by-step walkthroughs of Three-Figure Bearings with clear methods and exam tips.
Frequently Asked Questions
Three figures create a standard format, so 45° is written as 045°.
Bearings are always measured clockwise from North.
The bearing of East is 090°.
Add 180° if the bearing is below 180°, or subtract 180° if it is above 180°.
