Bearing Vectors of a Plane Against Wind

[Mel Gibson]

Hello!

I am trying to solve this problem about the vectors of an airplane against wind for my precalc class. I've done problems similar to this where you create a triangle using the resulting angle and wind, and solve with the Law of Sines--but I don't understand what's going on in this one. I believe I have a good picture for the first part, but it's the second part I'm mostly stuck with. What's the information I'm supposed to use to write the vectors in component form? Also, why would they need to include theta, isn't the plane bearing directly north? I think my knowledge of vectors may just be spotty in general. Anyways, I would really appreciate some help with this, so thank you to anyone who can!
-Mel Gibson

 

[skeeter]

air vector + wind vector = track (or ground) vector

the problem states the desired track is due north

the wind is blowing from the northeast (that would be in the southwest direction), which means the plane should steer (the air vector) into the wind to maintain the desired track.

see what you can do with the attached diagram ...