Question

Find the distance in kilometers between the following pair of cities, assuming they lie on the same north-south line. The radius of the Earth is approximately 6400 km. City A at 15° N, and City B at 45' S (round your answer to the nearest km)

Answer 1

The latitude of each city is an angle measured from the center of the Earth. Since the cities lie on the same north-south line, we can model the Earth as a flat circle:

The angle between the cities A and B is:

`15^(\circ)+45^(\circ)=60^(\circ)`

On any circle, the length of an arc is equal to the angle in which that arc lies, multiplied by the radius of the circle (provided that the angle is measured in radians).

Write the angle of 60° in radians, since 180° are equal to π radians:

`60^(\circ)*\frac{\pi\text{rad}}{180^(\circ)}=(\pi)/(3)\text{rad}`

Multiply the angle between the cities A and B (which is π/3) by the radius of the Earth to find the distance between those cities over the curved surface of the Earth: