Bearings (CIE IGCSE Maths: Extended)

What are bearings?

• Bearings are a way of describing and using directions as angles
• They are specifically defined for use in navigation because they give a precise location and/or direction

How are bearings defined?

• There are three rules which must be followed every time a bearing is defined
  
  • They are measured from the North direction

    North is usually straight up in terms of a scale drawing or map drawn on a piece of paper and should be shown somewhere on the diagram

  • They are measured clockwise (from North)
    If you get muddled up look at a clock on the wall

  • The angle should always be written (said) with 3 figures
    So angles under 100° should have zero to fill in the missing figures, eg 059, 008

• Notice also that the degree symbols are not usually included when talking about bearings

What are bearings used for?

• Bearings questions will normally involve the use of Pythagoras or trigonometry to find missing distances (lengths) and directions (angles) within navigation questions
  • You should always draw a diagram
• There may be a scale given or you may need to consider using a scale
• Some questions may involve the use of angle facts to find the missing directions
• To answer a question involving drawing bearings the following steps may help:
  • STEP 1: Draw a diagram adding in any points and distances you have been given
  • STEP 2: Draw a North line (arrow pointing vertically up) 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 3: Measure the angle of the bearing given from the North line in the clockwise direction
  • STEP 4: Draw a line and add the point B at the given distance
• You will likely then need to use Pythagoras's theorem or trigonometry to calculate another distance

How are bearings used on maps?

• If you need to use a map to find a direction, use a protractor to find the angle
  • Always begin by drawing the North line
  • Measure the angle clockwise from North
  • Write the angle using 3 figures 
• Knowing the compass directions for the common directions is helpful 
  • Due east means on a bearing of 090°
    • Draw the line directly to the right
  • Due south means on a bearing of 180°
    • Draw the line vertically downwards
  • Due west means on a bearing of 270°
    • Draw the line directly to the left
  • Due north means on a bearing of 360° (or 000°)
    • Draw the line vertically upwards
• Other directions can be found using these, for example 
  • Due Northeast means on a bearing of 045°
    
    • This is halfway between North (000°) and East (090°) 
  • Due Southeast means on a bearing of 135°
  • Due Southwest means on a bearing of 225°
  • Due Northwest means on a bearing of 315°

• Using the above bearings for compass directions will help you to estimate angles for other bearings on the map