trig
posted by ale on .
An aifplane is flying on a compass heading (bearing) of 170* at 460 mph. A wind is blowing with the bearing 200* at 80mph. a) Find the component form of the velocity of the airplane. b) Find the actual ground speed and direction of the airplane.

The way you have worded the problem, with the word "bearing",
460 mph at bearing 460 mph is the actual ground speed and direction of the airplane.
I suspect that they meant 460 mph at 170 to be the air speed and heading of the place, and that they want you to solve for the ground speed and direction by adding the wind velocity vector.
In that case:
ground speed components are:
Vy (north component) = 460 cos 170 + 80 cos 200 = 528.19 mph
Vx(east component) = 460 sin170 + 80 sin200 = 52.52 mph
Ground speed = 530.79 mph
bearing = arctan Vx/Vy = 174.2 degrees 
An airplane flying at 550 mph has a bearing of N 58 E. After flying for 1.5 hours, how far north and how far east has the plane traveled from its point of departure?

harghargharg

d = 550mi/h[N58oE] * 1.5h = 825mi[N58oE]825*Cos58 = 437 mi. N.
825*sin58 = 700 mi E.