GCSE Maths • Statistics • Primarily higher tier
GCSE Bearings Revision Guide
Build confidence with three-figure bearings, compass directions, accurate drawing and measuring, reverse bearings and exam-style navigation problems. Learn how bearings connect geometry, Pythagoras and trigonometry in Foundation and Higher Tier questions.
Foundation
Exam practice
Worked examples
What You'll Learn
Read Three-Figure Bearings
Interpret directions measured clockwise from North and write every bearing using three digits.
Draw and Measure Bearings
Draw a North line, place a protractor at the starting point, measure clockwise and draw the direction line accurately.
Find Reverse Bearings
Use the 180° relationship to find the direction back to the starting point.
Use Pythagoras and Trigonometry
Combine bearings with Pythagoras and SOHCAHTOA to calculate straight-line distances and angles.
Solve Exam-Style Problems
Sketch the journey, add North lines, label bearings and distances, choose a suitable method and check the final answer.
Key Bearing Rules
Clockwise measurement
Measure every bearing clockwise.
Start from North
Every bearing starts from a North line, with North pointing upwards.
Three-figure notation
Write bearings using three figures, including leading zeros: for example, 045° and 090°.
Reverse bearings
Add 180° when the bearing is less than 180°. Subtract 180° when the bearing is greater than 180°.
Accurate diagrams
Draw a clear sketch, add North lines, mark bearings and label distances before choosing a mathematical method.
Bearings Lessons
Three-Figure Bearings
Read compass directions and write angles measured clockwise from North using three figures.
Drawing and Measuring Bearings
Use a North line and protractor to measure clockwise and draw a required direction accurately.
Reverse Bearings
Find the direction back to a starting point by adding or subtracting 180°.
Bearings with Pythagoras and SOHCAHTOA
Use right-angled triangles to calculate straight-line distances and angles from North.
Multi-Step Bearings Exam Questions
Interpret a journey, draw a sketch, add North lines, label distances and select the mathematical method needed.
Worked Examples
Example 1: Write a Three-Figure Bearing
A direction is 45° clockwise from North. Write the bearing.
1:
Start from North and measure clockwise.
2. Write the angle using three figures: 45°.
2. Write the angle using three figures: 45°.
Example 2: Find a Reverse Bearing
A bearing is 230°. Find the reverse bearing.
1. The bearing is greater than 180°, so subtract 180°.
2. 230° − 180° = 50°.
2. 230° − 180° = 50°.
Example 3: Use Pythagoras
A boat travels 6 km East and then 8 km North. Find the straight-line distance from the start.
1. Draw a right-angled triangle..
2. Use Pythagoras: 6² + 8² = 100.
3. The straight-line distance is 10 km.
2. Use Pythagoras: 6² + 8² = 100.
3. The straight-line distance is 10 km.
Example 4: Use SOHCAHTOA
A ship is 15 km East and 20 km North of a harbour. Find the bearing from the harbour.
1. Find the angle from North: tan θ = 15/20.
2. θ ≈ 36.9°.
3. Round to the nearest degree and write the bearing using three figures: 37°.
2. θ ≈ 36.9°.
3. Round to the nearest degree and write the bearing using three figures: 37°.
Example 5: Multi-Step Distance and Bearing
A plane flies 40 km on a bearing of 090° and then 30 km North.
1. Draw a right-angled triangle.
2. Use Pythagoras: 40² + 30² = 2500, so the distance is 50 km.
3. Find the angle from North: tan θ = 40/30, so θ ≈ 53.1°.
4. Write the bearing using three figures: 53°.
2. Use Pythagoras: 40² + 30² = 2500, so the distance is 50 km.
3. Find the angle from North: tan θ = 40/30, so θ ≈ 53.1°.
4. Write the bearing using three figures: 53°.
- Common GCSE Mistakes
- Measuring anti-clockwise instead of clockwise.
- Forgetting to measure from North or omitting North lines from a diagram.
- Writing two-figure bearings instead of three-figure bearings.
- Adding or subtracting 180° incorrectly when finding a reverse bearing.
- Misreading a protractor or drawing an inaccurate diagram.
- Choosing the wrong trigonometric method.
- Exam Tips
- Read the question carefully and draw a clear sketch before calculating.
- Add North lines, mark all bearings and label every distance.
- Use a protractor regularly and practise measuring clockwise.
- Learn the main compass bearings and check that every answer has three figures.
- Revise Pythagoras and SOHCAHTOA so you can switch methods when a question requires it.
- Check the final answer and complete GCSE navigation and past-paper questions regularly.
Ready to Practice?
Printable Worksheet
Practise three-figure notation, compass bearings, reverse bearings and right-triangle navigation questions, with answers.
Interactive Quiz
Test clockwise measurement from North, leading zeros, reverse bearings and method selection.
Exam-Style Questions
Build confidence with ships, aircraft, distances, angles and multi-step bearings problems.
Watch the Bearings Tutorial
Follow a clear, step-by-step explanation of measuring clockwise from North, writing three-figure bearings, drawing bearings, finding reverse bearings and solving navigation problems with Pythagoras and SOHCAHTOA.
- Foundation and Higher Tier guidance
- Worked examples with distances and angles
Continue Your GCSE Maths Revision
Frequently Asked Questions
A bearing describes direction using an angle measured clockwise from North. It is always written using three figures, even when the angle is less than 100°.
East is 90°, South is 180° and West is 270°.
Draw a North line, place a protractor at the starting point, measure clockwise, mark the required angle and draw the direction line.
Add 180° when the original bearing is less than 180°. Subtract 180° when it is greater than 180°. The result is the direction back to the starting point.
Higher Tier questions can combine bearings with Pythagoras, SOHCAHTOA, the Sine Rule and the Cosine Rule to calculate distances and angles.
Source Practice Questions and Answers
Three-Figure Bearings
- 1. What is the bearing of East?
- 2. What is the bearing of South?
- 3. What is the bearing of West?
- 4. Write the bearing for a direction 35° clockwise from North.
- 5. Find the reverse bearing of 80°.
- 6. Find the reverse bearing of 300°.
Answers: 1. 90°; 2. 180°; 3. 270°; 4. 35°; 5. 260°; 6. 120°
Bearings Exam Questions
- 1. Find the reverse bearing of 70°.
- 2. Find the reverse bearing of 240°.
- 3. A ship travels 5 km East and 12 km North. Find the straight-line distance.
- 4. A plane travels 9 km East and 12 km North. Find the straight-line distance.
- 5. A ship is 10 km East and 20 km North of a port. Find the bearing from the port.
- 6. A plane is 15 km East and 15 km North of an airport. Find the bearing from the airport.
