GCSE · Bearings

Bearings & back bearingsExam-style questions

The three rules of a bearing, measuring from North at each new point, the ±180° back-bearing rule, and combining bearings with right-angled trigonometry to find distances and directions.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
A yacht sails from $P$ on a bearing of $070°$ for $12$ km to reach $Q$ . It then sails on a bearing of $160°$ for $9$ km to reach $R$ .Diagram NOT accurately drawn

(a) Show that angle $PQR$ is a right angle.

(b) Work out the distance $PR$ .

(c) Work out the bearing of $R$ from $P$ . Give your answer correct to the nearest degree.
Level 5 · 7 marksTry it
2
A ship leaves a harbour $H$ and sails $15$ km on a bearing of $048°$ to a point $A$ .

It then sails $25$ km due South to a point $B$ .

(a) Work out the distance $HB$ . Give your answer correct to 1 decimal place.

(b) Work out the bearing of $B$ from $H$ . Give your answer correct to the nearest degree.
Level 5 · 7 marksTry it
3
A ship leaves a harbour $H$ and sails $11$ km on a bearing of $062°$ to a point $A$ .

It then sails $8$ km on a bearing of $145°$ to a point $B$ .Diagram NOT accurately drawn

(a) Show that angle $HAB = 97°$ .

(b) Work out the distance $HB$ . Give your answer correct to 1 decimal place.

(c) Work out the bearing of $B$ from $H$ . Give your answer correct to the nearest degree.
Level 5 · 8 marksTry it