A ship sets sail from port A (86\(^o\)N, 56\(^o\)W) for port B (86\(^o\)N, 64\(^o\)W), which is close by. Find the distance the ship covered from port A to port B, correct to the nearest km.
[Take \(\pi\) = 3.142 and R = 6370 km]
A
62 km
B
97 km
C
389 km
D
931 km
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
AB = \(\frac{θ}{360}\times 2\pi Rcos\propto\) (distance on small circle)
= 64 - 56 = 8\(^o\)
\(\propto = 86^o\)
⇒ AB = \(\frac{8}{360}\) x 2 x 3.142 x 6370 x cos 86
⇒ AB = \(\frac{22,338.29974}{360}\)
∴ AB = 62km (to the nearest km)
Source: WAEC / JAMB / NECO Classroom Archive (Record #67398)