Determine the distance on the earth’s surface between two town P (lat 60°N, Long 20°E) and Q(Lat 60°N, Long 25°W) (Radius of the earth = 6400km)

A.
(frac{800pi}{9})km 
B.
(frac{800sqrt{3pi}}{9})km 
C.
800(pi) km 
D.
800(sqrt{3pi}) km
Correct Answer: Option C
Explanation
Angular difference ((theta))= 25° + 20° = 45°
(alpha) = common latitude = 60°
(S = frac{theta}{360°} times 2pi R cos alpha)
(S = frac{45°}{360°} times 2 pi times 6400 times cos 60°)
= (frac{6400pi}{8} = 800pi km)