A plain leaves airport A and travels 560 miles to airport B

A plain leaves airport A and travels 560 miles to airport B on a bearing of N36 degree E. The plane later leave airport B and travels to airport C 380 miles away on bearing of S74 degree E. Find the distance from airport A to airport C to the nearest tenth of a mile. The distance from airport A to airport C is about miles

Solution

1st distance covered = 560 (sin36 i^ + cos36 j^)

2nd distance covered = 380 (sin74 i^ - cos74 j^)

total distance covered = (560sin36 + 380sin74)i^ + (560cos36 - 380cos74)j^

= (694.44 i^ + 348.31 j^) miles

total distance from A to C =  sqrt(694.44² + 348.31²) = 776.894 miles