JAMB 1988 · UME · Q40

Elevation, depression & bearings

Alero starts a 3 km walk from $P$ on a bearing of $023^\circ$ . She then walks 4 km on a bearing of $113^\circ$ to $Q$ . What is the bearing of $Q$ from $P$ ?

Worked solution (try it first)

The bearings $023^\circ$ and $113^\circ$ differ by $90^\circ$ , so the two legs meet at a right angle.
The angle at $P$ between the first leg and $PQ$ has $\tan = \frac{4}{3}$ , so it is $53^\circ8'$ .
$Q$ is clockwise from the first leg, so add: the bearing is $023^\circ + 53^\circ8' = 076^\circ8'$ , option C.

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