Measure, draw and calculate three-figure bearings, including back bearings and angles between routes. It is on Foundation and Higher, aimed at grade 4. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A bearing is an angle measured clockwise from north, written as three figures: 047∘, not 47∘. To find a bearing of B from A, stand at A, face north, turn clockwise until you face B. The bearing of A from B is not the same number — it differs by 180∘ (add or subtract 180 to stay between 0 and 360).
Scale drawing bearings need a north line at the start point and a protractor. Combined with Pythagoras or trigonometry, a bearing question becomes a right-angled triangle with north and east as the axes. Keep 'from' clear: the from-point is where you stand.
A bearing is a three-figure angle measured clockwise from north. The reverse bearing is +180∘ or −180∘ so it stays between 000∘ and 360∘. Sketch north lines at both ends of the journey so the co-interior 180∘ is visible.
Objectives
Bearings are written with three digits: 040°, not 40°.
Draw a north line at the point you are measuring from.
The opposite direction differs by 180°.
Key points
Write bearings as three figures measured clockwise from north (for example 065∘).
Measure a bearing with a protractor from a north line at the correct point.
Find the back bearing (of A from B when you know B from A) by adding or subtracting 180.
Use parallel north lines and angle facts to find angles between routes.
Worked examples
Example 1
The bearing of B from A is 020°. Work out the bearing of A from B.
2 marks
The bearing is 20°, which is less than 180°, so add 180°.
20° + 180° = 200°.
The return bearing is 200°.
Answer: 200
Common slips
Slip: The bearing is 22°, which is less than 180°, so add 180°. That changes a number from the question, so it answers a different question.
Slip: 23° + 180° = 200°. That changes a number in the working, so the step no longer follows from the one before.
Slip: The return bearing is 204°. That does not match the working above it.
Example 2
The bearing of Y from X is 211°. Work out the bearing of X from Y.
2 marks
The bearing is 211°, which is 180° or more, so subtract 180°.
211° − 180° = 31°.
The return bearing is 031°.
Answer: 031
Common slips
Slip: The bearing is 213°, which is 180° or more, so subtract 180°. That changes a number from the question, so it answers a different question.
Slip: 214° − 180° = 31°. That changes a number in the working, so the step no longer follows from the one before.
Slip: The return bearing is 35°. That does not match the working above it.
Example 3
The bearing of B from A is 114°. The bearing of C from A is 169°. Work out angle BAC.
2 marks
Both bearings are measured from A, so angle BAC = 169° − 114°.
169 − 114 = 55.
Angle BAC = 55°.
Answer: 55
Common slips
Slip: Both bearings are measured from A, so angle BAC = 171° − 114°. That changes a number from the question, so it answers a different question.
Slip: 169 + 114 = 283. That uses addition, but this step needs subtraction.
Slip: Angle BAC = 59°. That does not match the working above it.
Questions and answers
GCSE Maths bearings questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
The bearing of B from A is 040. What is the back bearing of A from B?
Show answer
Answer: 220
Add 180 for the opposite direction.
This result stays below 360.
M1 — Add 180 for the opposite direction.
A1 — Answer 220
Question 2 Easy2 marks
One bearing is 030 and another bearing is 110. What is the angle between them?
Show answer
Answer: 80
Subtract the smaller bearing from the larger.
The value is 80.
M1 — Subtract the smaller bearing from the larger.
A1 — Answer 80
Question 3 Medium2 marks
What is the three-figure bearing for an angle of 7 degrees clockwise from north?
Show answer
Answer: 007
Bearings under 100 keep a leading zero.
The value is 007.
M1 — Bearings under 100 keep a leading zero.
A1 — Answer 007
Question 4 Medium2 marks
A journey goes 6 km due east and then 8 km due north. How far is the straight-line distance back to the start?
Show answer
Answer: 10
East and north are perpendicular.
Use Pythagoras for the straight-line distance.
M1 — East and north are perpendicular.
A1 — Answer 10
Question 5 Hard2 marks
The clockwise bearing from north is 050. How many degrees is the anticlockwise angle from north to that same direction?
Show answer
Answer: 310
A full turn is 360 degrees.
Subtract the clockwise bearing.
M1 — A full turn is 360 degrees.
A1 — Answer 310
Question 6 Hard2 marks
A ship sails on a bearing of 040. How many degrees is that direction from due east?
Show answer
Answer: 50
Due east is a bearing of 090.
Subtract the given bearing from 090.
M1 — Due east is a bearing of 090.
A1 — Answer 50
Question 7 Exam-style2 marks
A ship sails on a bearing of 050. How many degrees is that direction from due east?
Show answer
Answer: 40
Due east is a bearing of 090.
Subtract the given bearing from 090.
M1 — Due east is a bearing of 090.
A1 — Answer 40
Common mistakes
Most lost marks on this topic are one slip.
Measuring anticlockwise.
Bearings are clockwise from north.
Forgetting the opposite direction is 180° away.
Add 180°, then subtract 360° if the result is 360° or more.
Writing 40° instead of 040°.
Use three figures.
Spot the slip
A bearing is measured
clockwise from north
anticlockwise from east
from the nearest axis
Show the slip
clockwise from north North is 000. The angle turns clockwise.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Draw a north line at every point before you measure anything; this also helps the examiner give method marks.
For back bearings the marks are for ±180 — show that step.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.