City B is due north of city A. City A has a latitude of 14.6 degrees N, and city B has a latitude of 47.2 degrees N. find the distance in kilometers between the cities.
To find the distance between two cities given their latitudes, you can use the formula for calculating the great-circle distance. The great-circle distance is the shortest distance between two points on a sphere, such as the Earth.
The formula for calculating the great-circle distance is:
Distance = (Arc Length) x (Radius)
Where:
- Arc Length = 2π x (Δϕ/360) x (Radius of the Earth)
- Δϕ = Absolute difference in latitude between the two cities (in degrees)
- Radius = Radius of the Earth
Let's plug in the values for the given information to find the distance between city A and city B:
Δϕ = 47.2 - 14.6 = 32.6 degrees
Radius of the Earth = 6,371 kilometers (average radius of the Earth)
Using the formula:
Distance = (2π / 360) x Δϕ x Radius
Substituting in the values:
Distance = (2π / 360) x 32.6 x 6,371
Now, we'll calculate the distance:
Distance = (0.0174533) x 32.6 x 6,371
Distance = 3543.5 kilometers (rounded to one decimal place)
Therefore, the distance between city A and city B is approximately 3543.5 kilometers.