# Peshawar in Pakistan and Columbia in SC, USA are at the same latitude 54^o N. Their longitudes are 71.7^o E and 81.1^o W. The radius of the Earth at this latitude is nearly 6371 km. How do you find the latitude-circle distance between the two cities?

Aug 23, 2016

$9987 k m$, nearly.

#### Explanation:

The radius of the latitude circle of latitude ${\theta}^{o}$ is

(Radius of the Earth at latitude theta) X cos theta.

Here, this is $6371 X \cos {54}^{o}$= 3744.8 km, nearly.

The latitude-circle arcual distance between two places of longitudes

differing by $\beta$ is

(Latitude circle radius) X (longitude difference $\beta$ in radian).

Here, it is

$3744.8 X \left(\frac{71.7 + 81.1}{180}\right) X \pi$ km

$= 9987 k m$