JAMB 1992 · UME · Q27

Longitude & latitude

Determine the distance on the earth's surface between two towns $P$ (lat. $60^\circ$ N, long. $20^\circ$ E) and $Q$ (lat. $60^\circ$ N, long. $25^\circ$ W). [Take the radius of the earth as 6400 km.]

Worked solution (try it first)

$P$ is east and $Q$ is west, so add the longitudes: $20^\circ + 25^\circ = 45^\circ$ .
The radius of the parallel of latitude $60^\circ$ is $6400\cos60^\circ = 3200$ km.
The arc length is $\frac{45}{360} \times 2\pi \times 3200 = \frac18 \times 6400\pi$
$= 800\pi$ km, option C.

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