Scottish National 5 Mathematics

National 5 Maths Bearings

Use three-figure bearings with trigonometry to find distances and directions.

Formula referenceMixed revisionPrintable worksheet

Formula reference

Check the National 5 rules and formulae linked to this topic.

Which method?

Match exam clues to a suitable method.

Before you start

  • Measure angles clockwise.
  • Start from a north line.
  • Write bearings with three digits.
National 5 Mathematics lesson

Explanation

A bearing describes direction as an angle measured clockwise from north.

Bearings use three figures, so 7° is written 007° and 85° is written 085°.

The reverse bearing points in the opposite direction. Add or subtract 180°, keeping the result between 000° and 359°.

Key formulae and rules

  • measure clockwise from north
  • write three digits
  • reverse bearing = bearing ± 180°

Watch out

Measuring anticlockwise.

Check

Check that the bearing is measured clockwise from North, uses three figures and agrees with the direction shown.

Exam tip

Draw a fresh north line at the point where each bearing is measured.

Calculator tip

Use degree mode and keep full calculator values until the final requested rounding.

Worked examples

Worked example 1

Write a bearing

A path is 45° clockwise from north.

  1. Begin at north.
  2. Measure clockwise 45°.
  3. Pad the angle to three digits.

Answer: The bearing is 045°.

Worked example 2

Find a reverse bearing

The bearing of B from A is 072°.

  1. The reverse direction is 180° away.
  2. 72 + 180 = 252

So: The bearing of A from B is 252°.

Worked example 3

Cross north

A boat turns 50° clockwise from bearing 330°.

  1. 330 + 50 = 380
  2. Subtract 360 to return to the bearing range.

Answer: The new bearing is 020°.

Watch out

  • Measuring anticlockwise.
  • Using fewer than three digits.
  • Giving an answer greater than 359°.