Question

Using satellite technology, the distance between two planes can be measured by keeping track of the angle between them and the distance of each plane to the tracking station. Assume plane 1 is 176.27 miles away d plane 2 is 222.34 miles away and the angle formed with the tracking station is 38.59. How far apart are the planes?

Answer 1

The best approach to this is to use the law of cosine which is stated as  
c2 = a2 + b2 â’ 2ab cos(C)
 distance a=176.27; distance b=222.34; angle C=38.59; distance c is the missing value. 
 Hence c²=176.27²+222.34² -2*176.27*222.34cos38.59°= 138.71 miles