WAEC 2025 · Paper 1 · Q45✱✱

The bearings of $Q$ and $R$ from $P$ are $030^\circ$ and $120^\circ$ . If $|PQ| = 12\text{ m}$ and $|PR| = 5\text{ m}$ , find $|QR|$ .

Worked solution (try it first)

The angle between the bearings at $P$ is $\angle QPR = 120^\circ - 30^\circ$
$= 90^\circ$ .
So $QR$ is the hypotenuse of a right-angled triangle: $QR^2 = 12^2 + 5^2 = 169$ .
So $|QR| = 13$ m, option B.