NECO 2022 · Paper 1 · Q45

Longitude & latitude

$X$ and $Y$ are two places on the equator and their longitudes are $165^\circ$ E and $67^\circ$ W respectively. What is the shortest distance between them? (Take $R = 6400$ km.)

Worked solution (try it first)

One place is east and one west, so add: $165^\circ + 67^\circ = 232^\circ$ .
That is more than $180^\circ$ , so the shorter way round is $360^\circ - 232^\circ = 128^\circ$ .
The equator is a great circle of radius 6400 km, so the arc is $\frac{128}{360} \times 2 \times \frac{22}{7} \times 6400$ .
That is about 14303.5 km, option B.

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