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National 5 Maths: Bearings

Course content

  • Use bearings with trigonometry to find a distance or direction

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.

Textbook page references


Recommended revision course


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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.

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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 Maths 
BrightRED 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 solutions 
Calculator 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
• 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
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Click here to study the bearings notes on National5.com.

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