A jetliner must maintain a true course of due north and a gr

A jetliner must maintain a true course of due north and a ground speed of 425 mph. The wind is blowing at 65 mph in the direction N81degreeE. What airspeed, correct to the nearest mph, and compass heading, correct to the nearest degree, should the pilot choose for his aircraft

Solution

Let, north is (+y) and east is (+x) then...
v(y) = 425 - 65*cos(81deg)=414.8 mph
v(x) = 65*sin(81deg)=64.19 mph
Theta = tan^-1[v(y)/v(x)] = tan^-1[414.8/64.9]=81.11 degree
Theta =81.11 degrees North from west