Use the information below to find the shortest distance from City A, latitude 40°40?N, longitude 86°47?W to City B, latitude 20°12?N, longitude 151°45?W.
The shortest distance between two points on Earth's surface can be determined from the latitude and longitude of the two locations. If location 1 has
(lat, lon) = ($\alpha_1,\beta_1$) and location 2 has (lat, lon) = ($\alpha_2,\beta_2$), the shortest distance between the two locations is approximated by the formula below, where r = radius of
Earth ? 3960 miles and all angles are expressed in degrees. Also N latitude and E longitude are positive angles while S latitude and W longitude are negative angles.
$\frac{2\pi}{360}r \cos^{-1}[(\cos \alpha_1 \cos \beta_1 \cos \alpha_2 \cos \beta_2)$
$+ (\cos \alpha_1 \sin \beta_1 \cos \alpha_2 \sin \beta_2) + (\sin \alpha_1 \sin \alpha_2)]$
The shortest distance from City A to City B is approximately ? miles.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to four decimal places as needed.)
