City Latitude Longitude The shortest distance between two points on Earth's surface can be determined from the latitude and longitude of the two locations. For example, if location 1 has (lat, lon) = (a1, B1) and location 2 has (lat, lon) = (a2, B2), the shortest distance between the two locations is approximately d = rcos'[(cos aj cos B1 cos a2 cos B2) + (cos aj sin B1 cos a2 sin B2) + (sin aj sin a2)] where r = radius of Earth 3960 miles and the inverse cosine function is expressed in radians. Also N latitude and E longitude are positive angles while S latitude and W longitude are negative angles. Chicago, IL 41°50'N 87°37'W Honolulu, HI 21°18'N 157°50'W Melbourne, 37°47'S 144°58'E Australia

Calculus: Early Transcendentals
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the shortest distance from Honolulu to Melbourne, Australia,latitude 37°47 S,longitude 144°58 E.Round your answer to the nearest mile.

City
Latitude Longitude
The shortest distance between two points on Earth's surface can be determined from the latitude and
longitude of the two locations. For example, if location 1 has (lat, lon) = (a1, B1) and location 2
has (lat, lon) = (a2, B2), the shortest distance between the two locations is approximately
d = rcos'[(cos aj cos B1 cos a2 cos B2) + (cos aj sin B1 cos a2 sin B2) + (sin aj sin a2)]
where r = radius of Earth 3960 miles and the inverse cosine function is expressed in radians. Also
N latitude and E longitude are positive angles while S latitude and W longitude are negative angles.
Chicago, IL
41°50'N
87°37'W
Honolulu, HI
21°18'N
157°50'W
Melbourne,
37°47'S
144°58'E
Australia
Transcribed Image Text:City Latitude Longitude The shortest distance between two points on Earth's surface can be determined from the latitude and longitude of the two locations. For example, if location 1 has (lat, lon) = (a1, B1) and location 2 has (lat, lon) = (a2, B2), the shortest distance between the two locations is approximately d = rcos'[(cos aj cos B1 cos a2 cos B2) + (cos aj sin B1 cos a2 sin B2) + (sin aj sin a2)] where r = radius of Earth 3960 miles and the inverse cosine function is expressed in radians. Also N latitude and E longitude are positive angles while S latitude and W longitude are negative angles. Chicago, IL 41°50'N 87°37'W Honolulu, HI 21°18'N 157°50'W Melbourne, 37°47'S 144°58'E Australia
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