Bearings

Here we will learn about bearings, including measuring bearings, drawing bearings and calculating bearings.

There are also bearings maths worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are bearings?

Bearings are angles, measured clockwise from north.

To measure a bearing, we must first know which direction is north.

This north direction is usually provided in the maths exam question. We then measure the required angle in a clockwise direction. All bearings need to be given in three figures, so if the angle measured is less than 100 degrees, we must start the three-figure bearing with a zero.

Example:

The diagram shows three points A, B and P.

The angles are measured clockwise from the north line. 

The bearing of A from P is 045^{\circ} . 

The bearing of B from P is 260^{\circ} .

Bearings are used by sailors and pilots to describe the direction they are travelling. They are also used on land by hikers and the military.

What are bearings?

How to draw bearings

In order to draw bearings:

1. Locate the point you are measuring the bearing from and draw a north line if there is not already one given.
2. Using your protractor, place the zero of the scale on the north line and measure the required angle clockwise, make a mark on your page at the angle needed.
3. Draw a line from the start point in the direction of the bearing. If you are producing a scale drawing and know the distance to locate a point use this scale appropriately.

Explain how to draw bearings

Related lessons on loci and constructions

Bearings is part of our series of lessons to support revision on loci and construction. You may find it helpful to start with the main loci and construction lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• Loci and construction
• Loci
• Constructions
• Perpendicular bisector
• Angle bisector
• Constructing triangles
• How to draw a hexagon
• How to construct a 30, 60, 45, 90 degree angle
• Constructions between points and lines

Bearings maths examples (drawing)

Example 1: drawing a bearing less than 180°

Draw a bearing of 050^{\circ}

1. Locate the point you are measuring the bearing from and draw a north line if there is not already one given.

2Using your protractor, place the zero of the scale on the north line and measure the required angle clockwise, make a mark on your page at the angle needed.

3Draw a line from the start point in the direction of the bearing. If you are producing a scale drawing and know the distance to locate a point use this scale appropriately.

Example 2: drawing a bearing more than 180°

Draw a bearing of 300^{\circ}

Locate the point you are measuring the bearing from and draw a north line if there is not already one given.

Using your protractor, place the zero of the scale on the north line and measure the required angle clockwise, make a mark on your page at the angle needed.

If you have a 180^{\circ} protractor, we need to subtract the bearing required from 360^{\circ}

360^{\circ} - 300^{\circ} = 60^{\circ} , so measure 60^{\circ} anticlockwise

Draw a line from the start point in the direction of the bearing. If you are producing a scale drawing and know the distance to locate a point use this scale appropriately.

Example 3: drawing a scale drawing with a bearing

Make a scale drawing of a point Q 8 km away from a point P on a bearing of 110^{\circ} from P, using a scale of 1 cm : 2 km.

Locate the point you are measuring the bearing from and draw a north line if there is not already one given.

Using your protractor, place the zero of the scale on the north line and measure the required angle clockwise, make a mark on your page at the angle needed.

If the angle is more than 180^{\circ} and you do not have a full circle protractor then you should subtract the required angle from 360^{\circ} , and then measure this angle anticlockwise from the north line.

Draw a line from the start point in the direction of the bearing. If you are producing a scale drawing and know the distance to locate a point use this scale appropriately.

If the scale is 1cm : 2km , we will need to measure 4 cm to locate Q.

How to calculate bearings

In order to calculate bearings:

1. Locate the points you are calculating the bearing from and to.
2. Using the north lines for reference at both points, use angle rules and/or trigonometry to calculate any angles that are required.
3. Read off the three-figure bearing required.

How to calculate bearings

Bearings maths examples (calculating)

Example 1: calculating a bearing around a point

Calculate the bearing of A from P.

Locate the points you are calculating the bearing from and to.

Using the north lines for reference at both points, use angle rules and/or trigonometry to calculate any angles that are required.

We need the angle around the point P clockwise from the north line. We know that angles on a straight line add to 180^{\circ}. 180^{\circ} + 53^{\circ} = 233^{\circ}

Example 2: calculating a back bearing

The bearing of B from A is 070^{\circ} . Calculate the bearing of A from B.

Locate the points you are calculating the bearing from and to.

Using the north lines for reference at both points, use angle rules and/or trigonometry to calculate any angles that are required.

Drawing a north line at B and extending the line from A to B shows us a corresponding angle. If we travel from A to B, we need to turn another 180^{\circ} to return back to A. 180^{\circ} + 70^{\circ} = 250^{\circ}

Example 3: calculate a bearing using SOHCAHTOA

A ship sails 7 km due east from a point P to point A. It then sails 3 km due south from A to point B. Calculate the bearing of B from P.

Locate the points you are calculating the bearing from and to.

Sketch the diagram to help visualise the problem.

Using the north lines for reference at both points, use angle rules and/or trigonometry to calculate any angles that are required.

Drawing a line from P to B forms a right angled triangle. Use trigonometry to find the angle APB. Then add this to 90^{\circ} .

{{\tan }^{-1}}\left( \frac{3}{7} \right)=23^{\circ} to the nearest degree (bearings are normally given to the nearest degree)

90^{\circ} +23{}^\circ =113^{\circ}

Common misconceptions

• Not giving bearings less than 100^{\circ} in three figures

E.g.

A bearing with an angle of 45^{\circ} must be given as 045^{\circ} .

• Using the anticlockwise angle as the bearing

A common error is to use the anticlockwise angle as the bearing.

E.g.

The bearing of B from A is 080^{\circ} , a common mistake would be to use the co-interior angle as the back bearing of A from B as 100^{\circ} , calculating clockwise, the bearing of A from B should be 260^{\circ} .

The next lessons are

• Angles in parallel lines
• Trigonometry
• SOHCAHTOA
• Sine rule
• Cosine rule

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