Bearings
A bearing gives a direction as an angle. Three rules make every bearing unambiguous, and back bearings and scale drawings follow from them.
Part 1 of 3: Learn it
In short
- Measure from north, clockwise, and write three figures: 045°, not 45°.
- "The bearing of B from A" means stand at A and face B.
- Back bearing: add 180° if the bearing is under 180°, otherwise subtract 180°.
Where this is in your specification
Spec points: DfE G15 (with R2 for scale drawings)
| Board | Topic: Constructions, loci and bearings |
|---|---|
| DfE content | G2, G15, R2 |
| AQA 8300 | Geometry and measures |
| Edexcel 1MA1 | Geometry and measures |
| OCR J560 | 8 Basic geometry; 10 Mensuration |
| Eduqas C300 | HG2, HG13, HG15 |
| Cambridge IGCSE 0580 | E4.2, E4.3, E6.1 |
| National 5 C847 75 | Trigonometric skills: bearings |
The three rules
- Start at north.
- Turn clockwise.
- Write the angle with three figures: 008°, 072°, 315°.
So east is 090°, south is 180°, west is 270° and south-west is 225°.
Measuring and drawing
Draw a north line at the point you are measuring from. Put the protractor's centre on that point and its zero on the north line. For a bearing over 180°, measure the angle anticlockwise from north and take it away from 360°, or measure from south and add 180°.
Back bearings
North lines at two points are parallel, so the bearing back from B to A differs by exactly 180°. If A to B is 065°, B to A is 245°. If A to B is 230°, B to A is 050°.
Bearings with scale drawings and trigonometry
In scale drawing questions, convert the real distance with the scale, then draw the bearing. In calculation questions, the north and east directions make right angles, so Pythagoras and SOHCAHTOA find distances and angles.
The bearing of P from Q is 300°. What is the bearing of Q from P?
Show the answer
300 − 180 = 120°.
Part 2 of 3: See it worked
Worked examples
Example 1
The bearing of a lighthouse L from a boat B is 312°. Find the bearing of B from L.
- 312 is more than 180, so subtract
- 312 − 180 = 132
Answer: 132°.
Example 2
A ship sails 8 km due east, then 6 km due south. Find its distance and bearing from the start.
- Distance: √(8² + 6²) = √100 = 10 km
- Angle below east: tan⁻¹(6 ÷ 8) = 36.9°
- Bearing = 90 + 36.9 = 126.9°
Answer: 10 km on a bearing of 127° (to the nearest degree).
Common mistakes
- Measuring anticlockwise, or from east.
- Writing two figures, such as 65° instead of 065°.
- Measuring from the wrong point: "from A" means the north line is at A.
- Adding 180° to a bearing over 180°, giving more than 360°.
Write south-west as a bearing.
Show the answer
225°.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
The bearing of P from Q is 300°. What is the bearing of Q from P?
300 − 180 = 120°.
Write south-west as a bearing.
225°.
On a map 1 cm stands for 5 km. Two towns are 7.4 cm apart. How far apart are they?
7.4 × 5 = 37 km.
Jobs that use this
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Full lessons and marked practice for this course are coming soon to Brainlag Learn. See courses