Question

Three deer, a, b, and c, are grazing in a field. deer b is located 64.9 m from deer a at an angle of 53.4 ° north of west. deer c is located 77.9 ° north of east relative to deer
a. the distance between deer b and c is 96.8 m. what is the distance between deer a and c

Answer 1

Make an illustration of the problem to aid you in analyzing your approach to solve this. As seen on the picture, it forms a triangle. Since the total interior angles of a triangle is equal to 180°, then the missing angle would be: 180 - 53.4 - 77.9 = 48.7°. Applying the Cosine Law,

x² = 64.9² + 96.8² - 2(64.9)(96.8)(cos 48.7°)
x = √5289.567
x = 72.7 meters