(Geography: estimate areas) Find the GPS locations for Atlanta, Georgia; Orlando, Florida;...

(Geography: estimate areas) Find the GPS locations for Atlanta, Georgia; Orlando, Florida; Savannah, Georgia; and Charlotte, North Carolina from www.gps-data-team.com/map/ and compute the estimated area enclosed by these four cities. (Hint : Use the formula in Programming Exercise 4.2 to compute the distance between two cities. Divide the polygon into two triangles and use the formula in Programming Exercise 2.19 to compute the area of a triangle.)

Programming Exercise 4.2

(Geometry: great circle distance) The great circle distance is the distance between two points on the surface of a sphere. Let (x 1, y 1) and (x 2, y 2) be the geographical latitude and longitude of two points. The great circle distance between the two points can be computed using the following formula:

d = radius × arccos(sin(x1) × sin(x2) + cos(x1) × cos(x2) × cos(y1 − y2))

Write a program that prompts the user to enter the latitude and longitude of two points on the earth in degrees and displays its great circle distance. The average earth radius is 6,378.1 km. The latitude and longitude degrees in the formula are for north and west. Use negative to indicate south and east degrees. Here is a sample run:

Programming Exercise 2.19

(Geometry: area ofa triangle) Write a program that prompts the user to enter three points (x1 , y1), (x2 , y2), (x3 , y3) of a triangle and displays its area. The formula for computing the area of a triangle is

Here is a sample run: