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## 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?