Question

Two cities have the same longitude. the latitude of city A is 6 degrees N and the latitude of city B is 34 degrees N. assume the radius of earth is 3960 miles. find the distance between the two cities.

Answer 1

The distance between city A at 6 degrees N and city B at 34 degrees N, sharing the same longitude, is found by converting the difference in latitude to radians and multiplying by the Earth's radius. This results in an approximate distance of 1935 miles.

Step-by-step explanation:

To calculate the distance between two cities with the same longitude but different latitudes, we can use the formula for the arc length on the surface of a sphere. Since we're given that the radii of the Earth is 3960 miles and that the difference in latitude is 34 degrees - 6 degrees = 28 degrees, we can find the distance by converting degrees to radians and using the radius of the Earth in the arc length formula.

First, we convert 28 degrees to radians: 28 degrees * (π / 180 degrees) ≈ 0.4887 radians.

Now we can calculate the arc length, which is the distance along the surface of the sphere: Distance = radius * central angle in radians. Insert the values into the formula: Distance = 3960 miles * 0.4887 radians ≈ 1935 miles.

Therefore, the distance between city A and city B is approximately 1935 miles.