National 5 Maths
Bearings in Trigonometry
Page sections 
- Topic content
- Textbook page numbers
- Key ideas
- Worked examples
- Past paper questions
- Worksheets
- Notes and videos
Topic content
- Use bearings with trigonometry to find a distance or direction
Textbook page numbers
- Zeta National 5+ Maths pp.231-232
- TeeJay Maths Book N5 pp.78, 83 and 88-89
- Leckie National 5 Maths pp.308-311
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Zeta National 5+ Maths
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Key ideas
- Bearings tell us the direction, on a map, of one point from another.
- Bearings are always measured clockwise from a line pointing north.
- Bearings are usually written as three-figure bearings. For example, 070° means 70°.
- The word "from" is really important. It tells us where the north line is. For example:
The bearing of B from A is 070°.
The bearing of A from B is 250°. - Note that the difference between 70° and 250° is 180°, a straight angle. That's because "from A to B" and "from B to A" are in exactly opposite directions.
Exam questions
- Trigonometry in right-angled triangles (SOH CAH TOA) sometimes appears in Nat 5 Maths exams, but it's actually a Nat 4 topic.
- For this reason, bearings are usually combined with either the sine rule or the cosine rule.
- You should be able to use the sine and cosine rules confidently before practising bearings questions.
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Example 1 (calculator)
The map, which is not to scale, shows three villages K, L and M.
- M is due north of L.
- The bearing of K from M is 234°.
Calculate the bearing of K from L.
Example 2 (calculator)
A boat leaves a port A and sails 22 km north to B.
It then turns and sails 70 km to C.
Finally, it sails 85 km back to A.
Calculate the bearing of A from C.
Example 3 (calculator)
Alan and Claire are in their garden, thinking about some possible improvements to its layout.
They stand back-to-back and then walk in different straight-line directions from the same starting point.
Alan walks 2.3 metres on a bearing of 60°. Claire walks 3.8 metres on a bearing of 110°.
How far apart are Alan and Claire now?
Example 4 (calculator)
SQA National 5 Maths 2014 P2 Q10
In a race, boats sail round three buoys represented by A, B, and C in the diagram below.
B is 8 kilometres from A on a bearing of 060°.
C is 11 kilometres from B.
A is 13 kilometres from C.
(a) Calculate the size of angle ABC.
(b) Hence find the size of the shaded angle.
Example 5 (calculator)
SQA National 5 Maths 2015 P2 Q13
In the diagram below P, Q and R represent the positions of Portlee, Queenstown and Rushton respectively.
Portlee is 25 kilometres due South of Queenstown.
From Portlee, the bearing of Rushton is 072°.
From Queenstown, the bearing of Rushton is 128°.
Calculate the distance between Portlee and Rushton.
Do not use a scale drawing.
Example 6 (calculator)
SQA National 5 Maths 2017 P2 Q10
In the diagram below D, E and F represent the positions of Dunbridge, Earlsford and Fairtown respectively.
Dunbridge is 15 kilometres west of Earlsford.
From Dunbridge, the bearing of Fairtown is 126°.
From Earlsford the bearing of Fairtown is 230°.
Calculate the distance between Dunbridge and Fairtown.
Do not use a scale drawing.
Example 7 (calculator)
SQA National 5 Maths 2018 P2 Q13
A ferry and a trawler receive a request for help from a stranded yacht.
On the diagram the points F, T and Y show the positions of the ferry, the trawler and the yacht respectively.
• FY is 7·2 kilometres.
• TY is 5·6 kilometres.
• FT is 10·3 kilometres.
• F is on a bearing of 240° from T.
Calculate the bearing of the yacht from the trawler.
Example 8 (calculator)
SQA National 5 Maths 2021 P2 Q7
A fishing boat and a yacht left a harbour at the point H.
The fishing boat travelled 3.4 kilometres on a bearing of 047° to the point F.
The yacht travelled 5.7 kilometres on a bearing of 115° to the point Y.
Calculate the distance between the fishing boat at F and the yacht at Y.
Example 9 (calculator)
SQA National 5 Maths 2025 P2 Q12
In the diagram A, B and C represent the positions of three checkpoints in an orienteering course.
• B is 250 metres east of A.
• The bearing of C from A is 131°.
• C is 200 metres from B.
Calculate the bearing of C from B.
Do not use a scale drawing.
Buy N5 Maths practice papers
Zeta: Five Practice Papers TOP CHOICECGP: N5 Maths Exam Practice
Leckie: Revision and Practice
Hodder: N5 Maths Practice Papers
Past paper questions
| • All past paper questions by topic |
|
• 2014 Paper 2 Q10 (with cosine rule) • 2015 Paper 2 Q13 (with sine rule) • 2017 Spec. P2 Q15 (with sine rule) • 2017 Paper 2 Q10 (with sine rule) • 2018 Paper 2 Q13 (with cosine rule) • 2021 Paper 2 Q7 (with cosine rule) • 2025 Paper 2 Q12 (with sine rule) |
| Standard Grade: Credit (1986–2013) • Exam questions and answers • More exam questions and answers |
| Intermediate 2 (2000–2015) • Triangle trigonometry (with answers) |
Buy our favourite N5 textbook
Zeta National 5+ Maths
Clear and comprehensive.
Progressive exercises.
Includes answers.
Buy from Zeta Press
Bearings worksheets
| D R Turnbull - worksheet • Bearings (with solutions) |
| Inverclyde Academy worksheet • Bearings (no answers) |
| Larkhall Academy exercises • Pages 12-14 Ex 8 (no answers) |
Buy N5 Maths revision guides
How to Pass N5 Maths TOP CHOICEBrightRED: N5 Maths Study Guide
CGP: N5 Maths Revision Guide
Notes and videos
| Videos - Maths180.com |
| Video - Mr Graham Maths |
| Video - YouKenMaths |
| Notes and videos - Mistercorzi |
| Notes - National5.com |
| Worked examples - Maths Mutt |
| • Revision notes - BBC Bitesize • Test yourself - BBC Bitesize |
Click here to study the bearings notes on National5.com.
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