Bearings
A bearing is a way of describing a direction as an angle measured clockwise from North, always written using three figures, for example 045 or 270. Bearings are a GCSE Geometry and Measures topic, often combined with scale drawings, Pythagoras or angle facts to find distances and directions between places.
Method
- Remember bearings are always measured clockwise from North and always written with three digits, for example 007 not 7.
- Sketch a diagram with a North arrow at the starting point if one is not already given.
- Use angle facts (angles on a straight line sum to 180 degrees, angles round a point sum to 360 degrees, alternate angles between parallel North lines are equal) to work out unknown angles.
- To find a back bearing (the bearing from B to A when you know the bearing from A to B), add 180 if the original bearing is less than 180, or subtract 180 if it is 180 or more.
- For distance problems, combine the bearing with Pythagoras or trigonometry using the angle you have found.
- Check your final bearing is between 000 and 360, written with three figures.
Worked example
The bearing of Leeds from Halifax is 065. Work out the bearing of Halifax from Leeds.
- Since 065 is less than 180, add 180 to find the back bearing.
- 065 + 180 = 245.
- Final answer: the bearing of Halifax from Leeds is 245.
Practice questions
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Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
The bearing of Oxford from Reading is 315. Work out the bearing of Reading from Oxford.
Connor lives in village A. J is a road junction. The bearing of village A from J is 032. The bearing of village B from J is 124. A, B and J form a triangle, and angle JAB = 46 degrees. Work out the size of angle ABJ.
A ship sails from port P on a bearing of 070 for 24 km to reach point Q. It then sails on a bearing of 340 for 18 km to reach point R. The journey from P to Q to R takes 1 hour 45 minutes in total. (a) Calculate the direct distance from P to R. (b) Calculate the average speed for the whole journey, in km/h.
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