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15.8 Bearings

GCSE Maths Foundation · Edexcel · Chapter 15: Constructions, Loci and Bearings

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: three-figure bearings, measuring and drawing bearings, back bearings and bearings in scale drawings. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Understand and write three-figure bearings
  • Measure and draw bearings with a protractor
  • Work out a back bearing using angle facts
  • Solve problems using bearings and scale drawings

Key words

  • Bearing: A direction given as an angle measured clockwise from north.
  • Three-figure bearing: A bearing written with three digits, e.g. 045° not 45°.
  • Back bearing: The bearing for the return journey, from B back to A.
  • North line: A line pointing due north, drawn at the point you measure from.

Three-figure bearings

A bearing has three rules: measure from north, turn clockwise, and write three figures. "The bearing of B from A" means stand at A, face north and turn clockwise until you face B.

Worked example: compass directions

Write south-east as a bearing.
South-east is halfway between east (090°) and south (180°).

Answer: 135°

Measuring and drawing bearings

Draw a north line at the point you are measuring from. Put the centre of the protractor on the point with 0° on the north line. For a bearing more than 180°, measure the angle anticlockwise from north and subtract it from 360°.

Worked example: a reflex bearing

From P, the angle measured anticlockwise from north to Q is 130°.
Bearing = 360° − 130° = 230°

Answer: bearing of Q from P = 230°

Worked example: drawing a bearing of 300°

300° is more than 180°, so measure 360° − 300° = 60° anticlockwise from the north line and draw the line.

Answer: a line pointing 60° west of north

Back bearings

The north lines at A and B are parallel, so you can use angle facts. The back bearing differs from the bearing by exactly 180°.

Key fact: If the bearing is less than 180°, add 180°. If it is 180° or more, subtract 180°.

Worked example: back bearings

(a) The bearing of B from A is 070°. Bearing of A from B = 070° + 180° = 250°.
(b) The bearing of D from C is 315°. Bearing of C from D = 315° − 180° = 135°.

Answer: (a) 250° (b) 135°

Bearings and scale drawings

Worked example: a boat trip

A boat sails 10 km from harbour H on a bearing of 040° to P, then 6 km due south to Q. Use a scale of 1 cm to 2 km.
Draw HP = 5 cm on 040°. At P, draw a new north line and draw PQ = 3 cm due south (180°).
Measure HQ: about 3.3 cm, so about 6.6 km. Measure the bearing of Q from H: about 076°.

Answer: Q is about 6.6 km from H on a bearing of about 076°

Common mistakes

  • Measuring anticlockwise, or from east instead of north.
  • Writing 45° instead of 045°. Bearings always have three figures.
  • Measuring at the wrong point: "from A" means the north line is at A.
  • Forgetting to draw a new north line at each point of a journey.

Revision questions

Try these, then check your answers below each one.

Question 1. Write the direction due west as a three-figure bearing (in degrees).

Answer: 270 °

Working: North 000°, east 090°, south 180°, west 270°.

Question 2. The bearing of B from A is 065°. Work out the bearing of A from B, in degrees.

Answer: 245 °

Working: 65 + 180 = 245°.

Question 3. The bearing of Q from P is 310°. Work out the bearing of P from Q, in degrees.

Answer: 130 °

Working: 310 - 180 = 130°.

Related lessons

Continue in the full course

This lesson is section 15.8 (EGCMF1508) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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