Los Angeles (32 degrees North, 119degrees West) and Atlanta (33 degrees North, 84 degrees West) are approximately at the same latitude but not longitude. If a crow were to fly between the two cities what is the approximate shortest flight distance in kilometers?
To find the approximate shortest flight distance between Los Angeles and Atlanta, we can use the Haversine formula, which calculates the great-circle distance between two points on the Earth's surface given their latitude and longitude coordinates.
First, we need to convert the latitude and longitude values from degrees to radians:
Los Angeles:
Latitude: 32 degrees = 32 * (π/180) = 0.5585 radians
Longitude: -119 degrees = -119 * (π/180) = -2.0769 radians
Atlanta:
Latitude: 33 degrees = 33 * (π/180) = 0.5759 radians
Longitude: -84 degrees = -84 * (π/180) = -1.4661 radians
Next, we can use the Haversine formula:
d = 2 * R * arcsin(sqrt(sin((lat2 - lat1)/2)^2 + cos(lat1) * cos(lat2) * sin((lon2 - lon1)/2)^2))
Where:
- d is the distance between the two points,
- R is the Earth's radius (mean radius = 6,371 kilometers),
- lat1 is the latitude of the first point (Los Angeles),
- lat2 is the latitude of the second point (Atlanta),
- lon1 is the longitude of the first point (Los Angeles),
- lon2 is the longitude of the second point (Atlanta).
Plugging in the values:
d = 2 * 6371 * arcsin(sqrt(sin((0.5759 - 0.5585)/2)^2 + cos(0.5585) * cos(0.5759) * sin((-1.4661 - (-2.0769))/2)^2))
Calculating this equation will give us the approximate shortest flight distance between Los Angeles and Atlanta.