Bearings
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Revision notes for AQA GCSE Maths Bearings. Open the guide for explanations and worked examples. Written against the AQA GCSE Maths (8300) specification, so the content matches what's examinable rather than general Maths background.

Bearings

What you'll learn

  • What a bearing is and why it is always written with three figures.
  • How to read a bearing from a diagram.
  • How to draw a bearing using a protractor.
  • How to find a reverse bearing, such as going back from B to A.

The basics you need first

A compass direction tells you which way something is facing. The main compass directions are North, East, South and West.

A North line is a line drawn upwards from a point and usually labelled N. It is the starting line for every bearing.

Clockwise means the direction the hands of a clock move: round to the right, then down, then left.

What is a bearing?

A bearing is a special angle used to describe direction.

Definition

Bearing

A bearing is an angle measured from North, going clockwise, and written using three figures, such as 067° or 125°.

A bearing is measured clockwise from the North line at the starting point.

Key Idea

The three bearing rules

  • Start measuring from North.
  • Measure clockwise.
  • Write the answer using three figures.

Reading a bearing from a diagram

When a question says “the bearing of B from A”, you start at A. The word from tells you where the angle begins.

Example

Reading a bearing from a diagram

Imagine point A has a North line drawn upwards. The line from A to B is to the right of North, and the clockwise angle from North to AB is 67°.

The bearing of B from A is the clockwise angle measured at A from North to AB.

  1. Start at A, because the bearing is of B from A.

  2. Look at the North line drawn at A.

  3. Turn clockwise from North until you are pointing along the line AB.

  4. The angle is 67°, so write it as a three-figure bearing: 067°.

Common Mistake

Mixing up from and to

In “the bearing of B from A”, you measure at A, not at B. If you measure at the wrong point, you usually find the opposite direction.

Three-figure bearings

A three-figure bearing always has three digits.

So:

  • 7° becomes 007°
  • 42° becomes 042°
  • 115° stays 115°

You add zeros at the front if the angle has fewer than three digits.

Tip

Leading zeros matter

If your bearing is less than 100°, check whether you need a zero at the front. For example, 58° must be written as 058°.

Example

Writing a small angle as a bearing

At point P, the clockwise angle from North to point Q is 34°. Write the bearing of Q from P.

A small clockwise angle from North is written as a three-figure bearing using a leading zero.

  1. The angle has been measured from North.

  2. It has been measured clockwise.

  3. The angle is 34°, which has only two digits.

  4. Add a zero at the front, so the bearing of Q from P is 034°.

Drawing a bearing

To draw a bearing, you usually need a ruler and a protractor. A protractor is the tool used to measure and draw angles.

The key idea is: draw the North line first, then measure clockwise from it.

Example

Drawing a bearing

Draw point Q so that it is 5 cm from P on a bearing of 120°.

A bearing of 120° is measured clockwise from North and places Q down and to the right of P.

  1. Draw and label point P.

  2. Draw a vertical North line upwards from P and label it N.

  3. Place the centre of your protractor on P.

  4. Line up 0° on the protractor with the North line.

  5. Measure 120° clockwise and make a small mark.

  6. Draw a straight line from P through the mark.

  7. Measure 5 cm along this line and label the point Q.

Tip

Check the direction

A bearing of 120° should point down and to the right, because it is more than 90° but less than 180°.

When the angle is on the other side of North

Sometimes a diagram shows a small angle going anticlockwise from North. Anticlockwise means the opposite direction to the hands of a clock.

That small angle is not the bearing. Bearings must go clockwise, so you need to go all the way round from North.

Example

Finding a bearing using 360°

At point C, the line to D is 35° anticlockwise from North. Find the bearing of D from C.

The marked 35° anticlockwise angle is not the bearing; the bearing is the clockwise angle all the way round from North to CD.

  1. Start at C, because the bearing is of D from C.

  2. The 35° angle goes anticlockwise, so it is not the bearing.

  3. A full turn around a point is 360°. Subtract the small angle from a full turn:

    360∘−35∘=325∘360^\circ - 35^\circ = 325^\circ360∘−35∘=325∘

  4. The bearing of D from C is 325°.

Common Mistake

Using the small anticlockwise angle

If the diagram shows 35° to the left of North, the bearing is not 035°. You must measure clockwise, so the answer is 325°.

Reverse bearings

A reverse bearing is the bearing for travelling back the other way.

For example, if you know the bearing of B from A, the reverse bearing is the bearing of A from B.

Definition

Reverse bearing

A reverse bearing points in the opposite direction. Opposite directions differ by 180°.

Reverse bearings are opposite directions, so their directions differ by 180°.

To find a reverse bearing:

  • If the bearing is less than 180°, add 180°.
  • If the bearing is more than 180°, subtract 180°.
Example

Finding the bearing back again

A walker travels from village V to tower T on a bearing of 072°. Find the bearing of V from T.

The return journey from T to V is the reverse bearing of the original 072° journey from V to T.

  1. The new bearing starts at T, because you are finding the bearing of V from T.

  2. This is the opposite direction to the original journey.

  3. Add 180° because 072° is less than 180°:

    072∘+180∘=252∘072^\circ + 180^\circ = 252^\circ072∘+180∘=252∘

  4. The bearing of V from T is 252°.

Example

Reverse bearing when the angle is large

A ship travels from A to B on a bearing of 230°. Find the bearing of A from B.

For a bearing greater than 180°, the reverse direction is found by looking back from B to A.

  1. You are now looking back from B to A.

  2. Opposite directions differ by 180°.

  3. Subtract 180° because 230° is more than 180°:

    230∘−180∘=050∘230^\circ - 180^\circ = 050^\circ230∘−180∘=050∘

  4. Write the answer with three figures: 050°.

Exam technique

In the exam

  1. Read the wording carefully: the point after from is where you measure the angle.

  2. Check the three bearing rules before writing your answer: North, clockwise, three figures.

  3. If you have found a small anticlockwise angle, use 360° minus that angle; if you need the reverse direction, add or subtract 180°.

Self review

Check yourself

  • Why is 35° written as 035° when it is a bearing?

  • If a bearing is measured at point A, which phrase tells you that in the question?

  • What calculation helps when the marked angle is anticlockwise from North?

Recap questions

Test yourself with 5 quick questions on this guide. Answer them all correctly to complete it.

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