Determine the distance on the earth's surface between two town P (lat 60^\circN, Long 20^\circE) and Q(Lat 60^\circN, Long 25^\circW) (Radius of the earth = 6400km)
A
\(\frac{800\pi}{9}\)km
B
\(\frac{800\sqrt{3\pi}}{9}\)km
C
800\(\pi\) km
D
800\(\sqrt{3\pi}\) km
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Angular difference (\(\theta\))= 25^\circ + 20^\circ = 45^\circ
\(\alpha\) = common latitude = 60^\circ
\(S = \frac{\theta}{360^\circ} \times 2\pi R \cos \alpha\)
\(S = \frac{45^\circ}{360^\circ} \times 2 \pi \times 6400 \times \cos 60^\circ\)
= \(\frac{6400\pi}{8} = 800\pi km\)
Source: Myschool Past Questions Archive (Record #31337)