Using satellite technology the distance between two planes can be measured by keeping track of the angles between them and the distances of each plane to the tracking station. assume plane 1 is 176.27 miles away and plane two is 222.34 miles and the angle formed with the tracking station is 38.59 degrees. how far apart is the planes

With the given in this item, the best way to solve for the distance between the planes is through the cosine law which can be mathematically expressed as,
                             c² = b² + a² - 2ab(cosC)
Substituting the given,
       c² = (176.27 mi)² + (222.34 mi)² - 2(176.27 mi)(222.34 mi)(cos 38.59°)
                            c = 138.71 mi
Thus, the distance between the two planes is approximately 138.71 miles.