WAEC 2009 · Paper 2 · Q9

(a)(i)
$A$ (lat $43^\circ$ N, long $77^\circ$ E), $B$ (lat $43^\circ$ N, long $103^\circ$ W) and $C$ (lat $57^\circ$ S, long $77^\circ$ E) are three points on the surface of the earth. Find the distance from $A$ to $B$ along latitude $43^\circ$ N. [Take $\pi = 3.142$ and $R = 6400$ km]
(a)(ii)
Find the distance from $A$ to $C$ along the great circle joining the two points.
(b)
In triangle $XYZ$ , $|XY| = 9$ cm, $|XZ| = 10$ cm and $\angle YXZ = 75^\circ$ . Find $|YZ|$ .

Worked solution (try it first)

$A$ and $B$ are on opposite sides of the Greenwich meridian: the longitude difference is $77^\circ + 103^\circ = 180^\circ$ .
The radius of latitude $43^\circ$ is $R\cos 43^\circ$ .
Distance $= \frac{180}{360} \times 2 \times 3.142 \times 6400\cos 43^\circ$ .
$= 3.142 \times 6400 \times 0.7314$
$= 14\,706.65$ km.

$A$ and $C$ are on the same meridian ( $77^\circ$ E), on opposite sides of the equator: the latitude difference is $43^\circ + 57^\circ = 100^\circ$ .
Distance $= \frac{100}{360} \times 2 \times 3.142 \times 6400$
$= 11\,171.56$ km.