课 13, 主题 5

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Bearings Aqa Foundation

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Exam code:8300

Bearings

What are bearings?

Bearings are a way of describing an angle
- They are commonly used in navigation
There are three rules which must be followed when using a bearing:
- They are measured from North
  - North is usually straight up on a scale drawing or map, and should be labelled on the diagram
- They are measured clockwise
- The angle should always be written with 3 digits
  - 059° instead of just 59°
Knowing the compass directions and their respective bearings can be helpful

How do I find a bearing between two points?

Identify where you need to start
- “The bearing of A from B” means start at B and find the bearing to A
- “The bearing of B from A” means start at A and find the bearing to B
Draw a North line at the starting point
Draw a line between the two points
Measure the angle between the North line and the line joining the points
- Measure clockwise from North
Write the angle using 3 figures

How do I draw a point on a bearing?

You might be asked to plot a point that is a given distance from another point and on a given bearing
STEP 1
Draw a North line at the point you wish to measure the bearing from
- If you are given the bearing from A to B draw the North line at A
STEP 2
Measure the angle of the bearing given from the North line in the clockwise direction
STEP 3
Draw a line and add the point B at the given distance

How do I find the bearing of B from A if I know the bearing of A from B?

If the bearing of A from B is less than 180°
- Add 180° to it to find the bearing of B from A
If the bearing of A from B is more than 180°
- Subtract 180° from it to find the bearing of B from A

How do I answer trickier questions involving bearings?

Bearings questions may involve the use of Pythagoras or trigonometry to find missing distances (lengths) and directions (angles)
- You should always draw a diagram if there isn’t one given

Examiner Tips and Tricks

Make sure you have all the equipment you need for your maths exams
- A rubber and pencil sharpener can be essential as these questions are all about accuracy
- Make sure you can see and read the markings on your ruler and protractor
Always draw a big, clear diagram and annotate it, be especially careful to label the angles in the correct places!

Worked Example

A ship sets sail from the point P, as shown on the map below.

It sails on a bearing of 105° until it reaches the point Q, 70 km away. The ship then changes path and sails on a bearing of 065° for a further 35 km, where its journey finishes.

Show on the map below the point Q and the final position of the ship.

Draw in a north line at the point P

Measure an angle of 105° clockwise from the north line

Making sure you are accurate, carefully make a small but visible mark on the map

Draw a line from P through the mark you have made. Make this line long so that you can easily measure along it accurately

Use the scale given on the map (1 cm = 10 km) to work out the number of cm that would represent 70 km

70 km = 70 ÷ 10 = 7 cm

Accurately measure 7 cm from the point P along the line and make a clear mark on the line
Label this point Q

A bearing of 065 means 65° clockwise from the North

First, draw a North line at the point Q, then carefully measure an angle of 65° clockwise from this line. Make a mark and then draw a line from Q through this mark

Using the scale, find the distance in cm along the line you will need to measure.

35 km = 35 ÷ 10 = 3.5 cm

Accurately measure 3.5 cm from the point Q along this new line and make a clear mark on the line
This is the final position of the ship.

Bearings worked example working solution

Maths Gcse Aqa Foundation