A jet is flying through a wind that is blowing with a speed

A jet is flying through a wind that is blowing with a speed of 55 mi/h in the direction N 30 degree E. The jet has a speed of 770 mi/h relative to the air. In what direction should the pilot head the plane for the true course to be due north? N _________ degree

Solution

Note that the jet heads in a direction 30° west of north, so the jet will be traveling at an angle of 900° + 30° = 120° with respect to the positive x-axis. Thus, the vector that represents the velocity of the jet is:
<770cos(120°), 770sin(120°)>.

The wind vector is 30° east of north, so this vector is just:
<55cos(60°), 55sin(60°)>.

Adding these two vectors together gives:
<770cos(120°) + 55cos(60°), 770sin(120°) + 55sin(60°)>
= <-357.5, 714.4710>.

This vector does have the required magnitude and direction. Maybe you calculated them wrong? The magnitude is:
|<-357.5, 714.4710>| = [(-357.5)^2 + (714.4710)^2] 7948.9212mph.

To find the direction, note that <-357.5, 714.4710> is in Quadrant II. Using right triangles, the angle that this vector makes with the negative x-axis is:
tan = 714.4710/357.5 ==> = 63.4180°,

which is equivalent to N(90 - 63.4180)°W = N26.5820°W.