Question

To find the distance between two points on the earth when their latitude and longitude are known a right triangle can be used for an excellent approximation if the points are not too far apart. Point A is at latitude 42°30'45' N longitude 75°38'45" W. and point B is at latitude 42°31'30" N, longitude 75°39'30" W. Find the distance from A to B in nautical miles. (One minute of latitude is one nautical mile.)

The distance from point A to B is _____ nautical miles.
(Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed)

Answer 1

To find the distance between two points on the Earth with known latitude and longitude, we can use the Haversine formula. Converting the values to decimal degrees, we can calculate the central angle and then multiply it by the Earth's radius to find the distance.

Step-by-step explanation:

To find the distance between two points on the Earth when their latitude and longitude are known, we can use the Haversine formula, which is a mathematical equation that gives the distance between two points on a sphere. The formula takes into account the Earth's radius and the difference in latitudes and longitudes between the two points. We can convert the latitude and longitude values from degrees, minutes, and seconds to decimal degrees for easier calculation.

For point A, the latitude is 42°30'45'' N, which is equivalent to 42.5125° N, and the longitude is 75°38'45'' W, which is equivalent to -75.6458° W. For point B, the latitude is 42°31'30'' N, which is equivalent to 42.5250° N, and the longitude is 75°39'30'' W, which is equivalent to -75.6583° W.

Using the Haversine formula:

1. Convert the latitude and longitude values from degrees, minutes, and seconds to decimal degrees.
2. Calculate the difference in latitudes and longitudes between the two points.
3. Convert the latitudes and longitudes to radians.
4. Apply the Haversine formula to calculate the central angle.
5. Multiply the central angle by the Earth's radius to find the distance between the two points.

After performing the calculations, the distance from point A to point B is approximately 0.80 nautical miles.