GCSE Maths revision · Geometry and measures

Bearings

Foundation and Higher

The idea

A bearing is an angle measured clockwise from north, written with three figures: $045^\circ$ , $230^\circ$ . The bearing back is $180^\circ$ more or less than the bearing there.

Draw a north line at the point you are measuring from.
Measure clockwise from that north line.
Back bearing: add $180^\circ$ if the bearing is under $180^\circ$ , otherwise subtract it.

Watch out Measure from the north line at the starting point, not at the end point.

See it worked

Worked exampleNon-calculator3 marks

A map is drawn to a scale of 1 cm to 5 km.

(a) Two towns are 4.6 cm apart on the map. Work out the real distance between them.

(b) A lighthouse is due south-east of a port. Write down the bearing of the lighthouse from the port.

(a) Each centimetre is 5 km: $4.6 \times 5 = 23$ .
(b) South-east is half way between east ( $090^\circ$ ) and south ( $180^\circ$ ), measured clockwise from north.

Answer (a) 23 km; (b) $135^\circ$

Your turn

Question 1Non-calculator2 marks

The diagram shows the positions of two points, $A$ and $B$ .

The bearing of B from A is $074^\circ$ .

Work out the bearing of A from B.

Question 2Non-calculator4 marks

The diagram shows three points, $A$ , $B$ and $C$ .

From A, B is on a bearing of $055^\circ$ and C is on a bearing of $125^\circ$ . AB = AC = 9 km.

(a) Find angle BAC.

(b) Find angle ABC.

Question 3Calculator allowed5 marks

A walker leaves $A$ and walks 8 km on a bearing of $040^\circ$ to $B$ . She then walks 6 km on a bearing of $130^\circ$ to $C$ .

The diagram shows her route.

(a) Work out the bearing of $C$ from $A$ . Give your answer to the nearest degree.

(b) Write down the bearing of $A$ from $C$ .

In past papers

42 official questions in 42 papers since 2017. The latest:

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