Measurement and Bearings

Measurement and Bearings

Accurate measurement of lengths and angles is a practical geometric skill. Bearings provide a standardised way of stating direction, used in navigation and scale drawing contexts.

Measuring on Diagrams

  • Use a ruler to measure to the nearest mm; read from the 0 mark, not the end of the ruler.
  • Use a protractor to measure angles; place the centre hole on the vertex, align the baseline with one arm, and read off the angle of the other arm.
  • On scale drawings, measure on paper then multiply by the scale factor to find the real distance.

Bearings

A bearing is a direction measured clockwise from north, always written as a three-figure number (e.g. 045°, not 45°).

  • North = 000°, East = 090°, South = 180°, West = 270°.
  • The eight compass points: N, NE, E, SE, S, SW, W, NW — each 45° apart.
  • Back bearing (return bearing): add 180° to the forward bearing (if result ≥ 360°, subtract 360°).
N S W E NE SE SW NW B A 065° Bearing rules • From North • Clockwise • 3 figures • e.g. 065°

Back Bearings

If the bearing from A to B is \( \theta \), the bearing from B back to A is:

\[ \text{Back bearing} = \theta + 180° \quad (\text{if } \theta < 180°) \] \[ \text{Back bearing} = \theta - 180° \quad (\text{if } \theta \geq 180°) \]

 Key Takeaways

  • Bearings: always from North, always clockwise, always three figures (000° to 359°).
  • N=000°, E=090°, S=180°, W=270°. The eight compass points are 45° apart.
  • Back bearing: add 180° (subtract if over 360°).
  • On scale drawings: measure in cm, multiply by scale factor to get real distance.