4.3.8 How Far Away Is …? In this exercise, you will write a program to compute the distance between any two geo-locations. In this program, you will ask the user for four numbers: Starting latitude Starting longitude Ending latitude Ending longitude Then, using the GeoLocation class and our earlier example as a reference, compute the distance in miles between the two locations. A sample program run should match exactly as below: Enter the latitude of the starting location: 48.8567 Enter the longitude of the starting location: 2.3508 Enter the latitude of the ending location: 51.5072 Enter the longitude of the ending location: 0.1275 The distance is 208.08639358288565 miles.

Answer: See the Java program below (one file containing the main program and a GeoLocation class). It reads the four numbers, computes the great‑circle distance (in miles) and prints the result in the same format as the sample.

Explanation: This uses the spherical law of cosines to compute the central angle between two latitude/longitude points (converted to radians) and multiplies by the Earth radius in miles.

Code:

import java.util.Scanner;

public class Exercise4_3_8 {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);

        System.out.print("Enter the latitude of the starting location: ");
        double lat1 = input.nextDouble();
        System.out.print("Enter the longitude of the starting location: ");
        double lon1 = input.nextDouble();
        System.out.print("Enter the latitude of the ending location: ");
        double lat2 = input.nextDouble();
        System.out.print("Enter the longitude of the ending location: ");
        double lon2 = input.nextDouble();

        GeoLocation start = new GeoLocation(lat1, lon1);
        GeoLocation end = new GeoLocation(lat2, lon2);

        double distance = start.distanceTo(end);
        System.out.println("The distance is " + distance + " miles.");
    }
}

class GeoLocation {
    private double latitude;
    private double longitude;

    public GeoLocation(double latitude, double longitude) {
        this.latitude = latitude;
        this.longitude = longitude;
    }

    /**
     * Returns the distance between this location and another location in miles.
     * Uses the spherical law of cosines.
     */
    public double distanceTo(GeoLocation other) {
        double lat1 = Math.toRadians(this.latitude);
        double lon1 = Math.toRadians(this.longitude);
        double lat2 = Math.toRadians(other.latitude);
        double lon2 = Math.toRadians(other.longitude);

        double centralAngle = Math.acos(
            Math.sin(lat1) * Math.sin(lat2) +
            Math.cos(lat1) * Math.cos(lat2) * Math.cos(lon1 - lon2)
        );

        double earthRadiusMiles = 3958.7613; // average Earth radius in miles
        return earthRadiusMiles * centralAngle;
    }
}

Steps:

1. Read four doubles from the user (start latitude, start longitude, end latitude, end longitude).
2. Convert latitudes/longitudes to radians.
3. Compute the central angle using the spherical law of cosines.
4. Multiply the central angle by Earth’s radius in miles to get the distance.
5. Print the distance as shown.

If you prefer the haversine formula (more numerically stable for very small distances), I can provide that variant.