A small plane departs from point A heading for an airport 490 km due north at point B. The airspeed of the plane is 210 km/h and there is a steady wind of 50 km/h blowing directly toward the southeast.
(a) Determine the proper heading for the plane.
° west of north
(b) How long will the flight take?
Law of Sines/Cosines?
vf = vi + a*t
The Attempt at a Solution
So I drew a picture.
You need a velocity vector. This vector must be the sum of the velocity vectors of the wind and the plane, which should also be drawn on the sketch. So I drew a simple sketch showing the plane's northward trek, an angle [tex]\Theta[/tex], another vector showing the wind and the resulting vector. So:
The first vector points due North (up), from point A.
The wind vector points toward point A, at an angle [tex]\Theta[/tex].
The resultant vector points from point B to the non-pointed end of the wind vector.
...so where in the world does the trig come in? I just don't know where to start plugging in numbers, since this isn't a right triangle it isn't a simple sin/cos problem with the Pythag. Theorem, right?