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