Find the location of city C relative to the location of the starting point.?

Question

A commuter airplane starts from an airport and takes the route shown in Figure P3.17. The plane first flies to city A located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.

Answer 1

The plane starts at (0,0) and flies to point A(87.5sqrt(3),87.5)= A(151.6,87.5). It then flies to point B on a course that subtracts 150sin20 = 50.3 from the x-coordinate of A and adds 150 cos 20 = 140.95 to the y-coordinate of point A. So the plane is now at B(101.25, 228.5). It now flies 190 km due West to the point C(-88.75, 228.5).

So the plane is 21.2 degrees West of North at a distance of
245 km.

Answer 2

http://img529.imageshack.us/img529/2462/displtu5.jpg

89.7 km west and 228.5 km north

which is 245.5 km, 68.6° north of west of starting position