Final answer:
The shortest distance between two cities on the Earth can be found using the formula for the great circle distance.
Step-by-step explanation:
The shortest distance between two cities on the Earth can be found using the formula for the great circle distance, which is the shortest path between two points on a sphere. The formula is given by:
d = R * arccos(sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(long1 - long2))
where d is the distance, R is the radius of the Earth, lat1 and lat2 are the latitudes of the two cities, and long1 and long2 are the longitudes of the two cities.
Let's take an example. Suppose we want to find the shortest distance between Boston and New York City. The latitude and longitude of Boston are 42.3601° N and 71.0589° W, and the latitude and longitude of New York City are 40.7128° N and 74.0060° W. Plugging in these values into the formula, we get:
d = 6371 km * arccos(sin(42.3601°) * sin(40.7128°) + cos(42.3601°) * cos(40.7128°) * cos(71.0589° - 74.0060°))
Solving this equation will give us the shortest distance between Boston and New York City.