Trig Vector Question, What is the ground speed of the plane?

Question

An airplane has an airspeed of 500 kilometers per hour bearing N45°E. The wind velocity is 60 kilometers per hour in the direction N30°W. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane?

Answer 1

Find the component vectors along the coordinate axes and add. From trigonometry the speed components are;  five hundred km/hr N45(deg) is 500*sin(pi/4)=353.5534 (km/hr) N, 500*cos(pi/4)E = 353.5534 (km/hr) E. And the wind components are;  -60*sin(pi/4) N=  -51.9645 N, 60*cos(pi/6) E = 30 km/h E. The resultant ground speed is

53.5534-51.9645)N, (353.9645+15)E = (301.5919N, 383.5543E).

Finally from Pythagoras and Trigonometry the ground speed

Vg=  487.9251km/hr in the direction N51.821degE.