NECO 2023 · Paper 1 · Q44

Elevation, depression & bearings

An aeroplane flies from a town $P$ on a bearing of $045^\circ$ to a town $Q$ , a distance of $200\text{ km}$ . It then changes course and flies to another town $R$ on a bearing of $120^\circ$ . If $R$ is directly east of $P$ , calculate $|PR|$ , correct to the nearest km.

Worked solution (try it first)

On $045^\circ$ , $Q$ is $200\sin45^\circ \approx 141.4$ km east and $200\cos45^\circ \approx 141.4$ km north of $P$ .
$R$ is due east of $P$ , so the second leg must come back 141.4 km south.
The bearing $120^\circ$ is $60^\circ$ from due south, so $QR\cos60^\circ = 141.4$ , giving $QR \approx 282.8$ km.
That leg goes $282.8\sin60^\circ \approx 244.9$ km east.
So $|PR| \approx 141.4 + 244.9 \approx 386$ km, option B.

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