Two airplanes cross each other at an angle of 49 degrees. Airplane A is 32 miles from the crossing while airplane B is 76 miles. What is the distance between them at two instant?

Answer 1

The above diagram shows where plane A and B can be located in relation to the point where their paths would cross (C). We want to know the distance between A and B (which is c). This forms a triangle, for which the information we are given is SAS (side-angle-side). This fits the Law of Cosines:

c² = a² + b² - 2ac cos C

c² = 32² + 76² - 2(32)(76) cos 49

c² ≈ 3608.93

c ≈ 60