Bearings

 

What Are Bearings?

Bearings are used to describe direction, especially in navigation and map reading.

There are three key rules when working with bearings:

Bearings are measured from the North line.

Bearings are measured clockwise.

Bearings are written as three-figure angles (e.g. $045\degree, 120\degree, 270\degree$).

Useful Compass Bearings:

North = $000\degree$

East = $090\degree$

South = $180\degree$

West = $270\degree$

 

 

Finding Bearings Between Two Points

To find the bearing of B from A:

1. Draw a North line at A.
2. Draw a line from A to B.
3. Measure the angle clockwise from North.
4. Write your answer as a three-digit number.

"The bearing of A from B" means you start at B and measure the angle towards A.

 

Drawing a Point on a Given Bearing

If you're asked to place a point using a bearing and distance:

1. Draw a North line at the starting point.
2. Measure the given angle clockwise from North.
3. Use the scale to mark the correct distance along that bearing.
4. Plot and label the new point.

 

Finding the Reverse Bearing

If you know the bearing from A to B, you can find the bearing from B to A by:

• Adding $180\degree$ if the original bearing is less than $180\degree$.
• Subtracting $180\degree$ if the original bearing is more than $180\degree$.

Example: If the bearing of A from B is $070\degree$, then the bearing of B from A is:

$$070\degree + 180\degree = 250\degree$$

 

Problem Solving with Bearings

Bearings questions can involve:

• Drawing accurate diagrams.
• Measuring bearings and distances.
• Using scales (e.g. 1 cm = 10 km).
• Applying trigonometry or Pythagoras' theorem.

Always:

• Draw clear North lines.
• Label all points and angles.
• Use equipment carefully (ruler, protractor, pencil).

 

Example

A ship sails from point P on a bearing of $105\degree$ for 50 km, then changes course and sails 25 km on a bearing of $055\degree$.

Draw the final position of the ship.

 

 

Step 1: Draw a North line at point P.

 

 

Step 2: Measure 105° clockwise from North and draw the direction line.

Step 3: Use the scale (e.g. 1 cm = 10 km) to measure 5 cm along the line and mark the point.

 

 

 

 

 

Step 4: Draw a North line at the point.

 

 

Step 5: Measure $55\degree$ clockwise from North, draw the direction, and measure 2.5 cm for the second leg of the journey.

 

 

The final mark shows the ship’s ending position.