Geometry & Measures
Grade 4-6Bearings
Bearings questions test whether you can measure and write an angle correctly as a three-figure bearing, and then combine that skill with angle facts such as angles on a straight line or in a triangle to solve more involved problems. This lesson covers writing a bearing, finding a back bearing, combining bearings with a given angle, and using bearings in triangle and interception problems.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Writing a bearing
A bearing measures the angle from north, turning clockwise, to the direction of interest, and is always written using three figures, adding leading zeros where needed (for example 008° or 065°). Compass directions can be converted to bearings: north is 000°, east is 090°, south is 180°, west is 270°, and directions such as south-east (135°) or north-west (315°) fall exactly between these.
An angle of 65° measured clockwise from north is written as the bearing 065°, using three figures with a leading zero.
Back bearings
The back bearing is the bearing in the opposite direction, from B back to A, when the bearing of B from A is known. If the original bearing is less than 180°, add 180° to find the back bearing. If the original bearing is 180° or more, subtract 180° instead.
The bearing of B from A is 072°. Since 072° is less than 180°, the back bearing (bearing of A from B) is 072 + 180 = 252°.
Combining bearings with angle facts
Many questions give a bearing and then an additional angle turned through, requiring the two to be added or subtracted depending on the direction of the turn. Triangle problems involving bearings often require finding a back bearing first, then using it alongside angle facts such as the angles in a triangle or in an isosceles triangle.
The bearing of B from A is 040°, and angle BAC is 25°, measured clockwise from AB. Since C is further clockwise than B, the bearing of C from A is 040 + 25 = 065°.
Bearings in triangle problems
When a bearing question forms a triangle, find any back bearings needed first, then use the fact that angles on a straight line sum to 180°, or that a triangle isosceles due to equal distances has equal base angles, to work out the required angle.
A ship sails from A to B on a bearing of 060°, then from B to C on a bearing of 140°. The back bearing of A from B is 060 + 180 = 240°, so angle ABC, between BA (240°) and BC (140°), is 240 - 140 = 100°.
Worked Examples
Three exam-style questions, fully solved.
The diagram shows the angle between north and the direction of B, measured clockwise at A, as 65°. Write down the bearing of B from A as a three-figure bearing.
Easy- 1.Write the angle measured clockwise from north using three figures
Answer: 065°
The bearing of B from A is 205°. Find the bearing of A from B.
Medium- 1.Since the bearing is 180° or more, subtract 180° to find the back bearing
- 2.Calculate 205 - 180
Answer: 025°
From a lighthouse C, the bearing of boat A is 150° and the bearing of boat B is 230°. The two boats are the same distance from the lighthouse (CA = CB). Find the bearing of B from A.
Hard- 1.Find angle ACB: 230 - 150 = 80°
- 2.Since CA = CB, triangle ACB is isosceles, so the base angles are equal: angle CAB = angle CBA = (180 - 80) ÷ 2 = 50°
- 3.Find the back bearing of C from A: 150 + 180 = 330°
- 4.Since B lies on the anticlockwise side of AC as seen from A, subtract the base angle: 330 - 50
Answer: 280°
Avoid These
The most common mistakes students make.
Forgetting to write a bearing using three figures, for example writing 65° instead of 065°.
Always adding 180° to find a back bearing, instead of adding 180° when the original bearing is less than 180° and subtracting 180° when it is 180° or more.
Adding an extra angle onto a bearing when it should be subtracted, or the other way round, without checking the direction of the turn described in the question.
In triangle bearing problems, forgetting to find the back bearing first before applying angle facts such as angles in a triangle.
Misreading a bearing diagram and measuring the angle from a direction other than north, or measuring anticlockwise instead of clockwise.
FAQ
Questions parents and students ask.
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