GCSE Maths · Geometry & measures

Bearings

Three-figure bearings - measuring and calculating bearings, back bearings, and bearings with trigonometry.

200 GCSE-style practice questions

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Bearings, explained point by point

Everything the GCSE specification expects you to be able to do, and how to actually do it - the same lesson a signed-in student studies from.

  1. Measure and draw three-figure bearings

    A bearing is measured FROM north, CLOCKWISE, and always written with three figures: due east is 090°, south-west is 225°. Draw the north line at the point you are measuring from first - everything hangs off it.

  2. Calculate bearings using angle facts and parallel lines, including back bearings

    North lines at different points are parallel, so alternate and co-interior angles carry bearings between them. The bearing back the way you came differs by 180°: if B is on a bearing of 070° from A, then A is on 250° from B - add 180, or subtract if that passes 360.

  3. Solve bearings problems with scale drawings

    Draw each leg in turn: north line, measure the bearing with a protractor, then the scaled distance along it. The answer - a distance and bearing home, say - is measured straight off the finished diagram, then converted back through the scale.

  4. Combine bearings with Pythagoras' theorem and trigonometry

    Perpendicular legs - say 8 km due east then 5 km due north - form a right-angled triangle: Pythagoras gives the direct distance and tan⁻¹ gives the angle, which you then convert into a bearing from north. On Higher, non-perpendicular legs bring in the sine and cosine rules.

Practice

Try a Bearings question

A GCSE-style original question from this topic. Have a go before you open the working - deciding on an answer first is what makes the working stick.

The bearing of a tower T from a gate G is 110°. Using a north line at the tower, work out the bearing of G from T with the angle facts for parallel north lines.

  1. 070°
  2. 250°
  3. 290°
  4. 110°
Show the answer and the working

Answer: 290°

The north lines at G and T are parallel, and co-interior angles let you reach the back bearing 110° + 180°.

  1. The north lines at G and T are parallel.
  2. Reversing the direction adds 180° to a bearing below 180°.
  3. 110 + 180 = 290, so the bearing of G from T is 290°.

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