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?

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Answer 1 · 2016-08-23T12:21:45

#9987 km#, nearly.

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( (71.7+81.1)/180) X pi # km

#= 9987 km#