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A ship sets sail from port A (86oN, 56oW) for p...

A ship sets sail from port A (86oN, 56oW) for port B (86oN, 64oW), which is close by. Find the distance the ship covered from port A to port B, correct to the nearest km.

[Take π = 3.142 and R = 6370 km]

A.

62 km

B.

97 km

C.

389 km

D.

931 km

Correct answer is A

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)