An airplane has an air speed of 560 kilometers per hour bear

An airplane has an air speed of 560 kilometers per hour bearnig N45\'E. The wind velocity is 60 kilometers per hour the direction of N30\'W/ To the nearest thenth, what is the ground speed of the plane? what is its direction?

Solution

A = <560cos(45°), 560sin(45°)> = <395.98, 395.98>
W = <60cos(120°), 60sin(120°)> = <-30, 51.96>

A+W = <365.98, 447.94>
|A+W| = ((365.98)² + (447.94)²) = 578.4 km/hr
= arctan(y/x) = arctan(447.94/365.98) = 50.75° = N39.25E

All I did to get from 50.75° to N39.25E was do 90° - 50.75° 39.25°, since 90° is North.