National 5 Maths
Bearings
Course content
- Use bearings with trigonometry to find a distance or direction
Textbook page references
- Zeta National 5+ Maths
pp.231-232 - TeeJay Maths Book N5 pp.78, 83 and 88-89
- Leckie National 5 Maths pp.308-311
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, the SQA usually combines bearings 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.
N5 Maths revision course
National5.com self-study courseSave £10 with discount code 'Maths.scot'
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.
Recommended student book
Zeta Maths: National 5 Maths Textbook
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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.
Recommended revision guides
How to Pass National 5 MathsBrightRED N5 Maths Study Guide
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.
N5 Maths practice papers
Non-calculator papers and solutionsCalculator papers and solutions
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.
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Past paper questions
| • All past paper questions by topic |
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• 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) |
Other great resources
| Videos - Maths180.com |
| Video - Mr Graham Maths |
| Video - YouKenMaths |
| Notes and videos - Mistercorzi |
Notes - National5.com  |
| Worked examples - Maths Mutt |
| Lesson notes - Maths 777 |
| • Revision notes - BBC Bitesize • Test yourself - BBC Bitesize |
| Worksheet - D R Turnbull |
| Worksheet - Inverclyde Academy |
| Exercises - Larkhall Academy Pages 12-14 Ex 8 |
Click here to study the bearings notes on National5.com.
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