JAMB Mathematics 2023 Paper

Concept:Distance along a parallel of latitude is the arc length of a small circle, calculated using the latitude angle.Explanation:The two ports lie on the same latitude, so the distance between them is the arc length along that parallel.The angular difference in longitude is $\Delta \lambda = 64^\circ - 56^\circ = 8^\circ$.The effective radius of the parallel at latitude $86^\circ$N is $R\cos 86^\circ$.Use the small-circle distance formula:$$AB=\frac{\Delta \lambda}{360^\circ}\times 2\pi R\cos 86^\circ$$Substitute $\Delta \lambda = 8^\circ$, $\pi = 3.142$, and $R = 6370$ km:$$AB=\frac{8}{360}\times 2\times 3.142\times 6370\times \cos 86^\circ$$$$AB=\frac{8}{360}\times 40029.08\times 0.06976$$$$AB\approx \frac{8}{360}\times 2792.4$$$$AB\approx 62.05\text{ km}$$Answer:The distance is $62$ km, correct to the nearest km.Therefore, the correct option is A.