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 is C

Angular difference (\(\theta\))= 25° + 20° = 45°

\(\alpha\) = common latitude = 60°

\(S = \frac{\theta}{360°} \times 2\pi R \cos \alpha\)

\(S = \frac{45°}{360°} \times 2 \pi \times 6400 \times \cos 60°\)

= \(\frac{6400\pi}{8} = 800\pi km\)