JAMB 1985 · UME · Q46

Longitude & latitude

Two points $X$ and $Y$ , both on latitude $60^\circ$ S, have longitudes $147^\circ$ E and $153^\circ$ W respectively. Find, to the nearest kilometre, the distance between $X$ and $Y$ measured along the parallel of latitude. (Take $2\pi R = 4 \times 10^4$ km, where $R$ is the radius of the earth.)

Worked solution (try it first)

$X$ is east and $Y$ is west, so the longitude difference one way is $147^\circ + 153^\circ = 300^\circ$ .
The short way round is $360^\circ - 300^\circ = 60^\circ$ .
The parallel of latitude $60^\circ$ has radius $R\cos60^\circ$ , so its length is $2\pi R\cos60^\circ = 40\,000 \times 0.5$
$= 20\,000$ km.
The arc for $60^\circ$ is $\frac{60}{360}$ of that: $\frac16 \times 20\,000 \approx 3333$ km, option E.

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