Question

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.)

          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.)

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) = (α1,β1) and location 2 has (lat, lon) = (α2,β2), 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.
(2π)/(360)r cos^-1[(cosα1 cosβ1 cosα2 cosβ2)
+ (cosα1 sinβ1 cosα2 sinβ2) + (sinα1 sinα2)]
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.)

Added by Carol S.

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