Vectors in the Plane: Plane+Wind question

[pugfug90]

Homework Statement

An airplane has an airspeed of 430 mph at a bearing of S 45 degrees E. If the wind is 35 MPH in direction of N 30 degrees E, find groundspeed and direction of plane.

Homework Equations

[[v]]([cos theta], [sin theta])

The Attempt at a Solution

430(cos 315,sin315)+35(cos30,sin30)=?<334.4,-286.6>
[[v]]=?~440..

Back of book says that the ground speed is 422.3.. and if i go the vector wrong, that means magnitude and direction will be wrong also.. Where did I go wrong?

 

[HallsofIvy]

If the numbers you give are correct, then you have it right. The ground speed is 440.3, not 422.3.

 

[pugfug90]

Hope you're right. This isn't the 1st time the book has a typo or something.