For the Earth, the length of one degree of longitude is given by the following e
ID: 112718 • Letter: F
Question
For the Earth, the length of one degree of longitude is given by the following equation: L = cos(latitude) times 111.3 km. The angular distance (D) from one latitude-longitude point (point A) to another latitude-longitude point (point B) is given by the following equation: cos D = [sin(lat A)* sin(lat B)] + [cos(lat A)* cos (lat B) * cos(difference in longitudes)]. Solving for D (by finding the arc-cosine of the right-hand result) will give an answer in degrees that, when multiplied by 111.2 km, gives the "great circle" distance in km.Explanation / Answer
6. Coordinates of Lubbock: 33.5779 N / 101.8552 W
Coordinates of Denver: 39.7932 N /104.9903 W
Cos D = [sin (lat A) * sin (lat B)] + [cos (lat A) * cos (lat B) * cos (difference in longitudes)]
= [sin 33.5779 * sin 39.7392] + [cos 33.5779 * cos 39.7392 * cos 3.1351]
= 0.35357 + 0.6396
= 0.99326
Thus, Great Circle Distance = 111.2 * 0.99326 Km = 110.45 Km
7. The great circle path will not be a straight line because of the sphericity of the Earth rather than its flatness. Consequently, distance between two points on a spherical surface is an arc (which is not a straight line). Thus, the great circle distance may be the shortest distance between two points on Earth but it is not a straight line.