WAEC 2025 · Paper 2 · Q3✱✱

(a)
In the diagram, $PQSR$ and $SRYZ$ are parallelograms and $PQYZ$ is a straight line. If $|QY| = 2\text{ cm}$ and $|RS| = 3\text{ cm}$ , find $|PZ|$ .
(b)
Towns $P$ and $Q$ lie on latitude $56^\circ\text{N}$ , with longitudes $25^\circ\text{E}$ and $95^\circ\text{E}$ . Find the distance $PQ$ along the parallel of latitude, correct to the nearest km. $\left[R = 6400\text{ km}, \pi = \frac{22}{7}\right]$

Worked solution (try it first)

Both towns are on latitude $56^\circ$ N, and the difference in longitude is $95^\circ - 25^\circ = 70^\circ$ .
Along the parallel: $PQ = \frac{70}{360} \times 2 \times \frac{22}{7} \times 6400 \times \cos 56^\circ$
$\approx 4374$ km.