How do I make a compensation vector?

[yamugushi]

Homework Statement

I'm currently doing an airplane project in pre-calc, it is physics related, but since it's in pre-calc I put it here.
The problem is I have a plane, it's going N74W, wind is going N20E, the resultant vector is 324mph, and N67W, how do I compensate?

Homework Equations

I remember going over it once in class but I really don't want to screw it up since this project (which is a lot bigger than just this problem) is supposed to be a big part of the grade.

The Attempt at a Solution

I think I'm just supposed to make a vector go NxW, but I'm not sure how to get it.

 

[HallsofIvy]

Homework Statement

I'm currently doing an airplane project in pre-calc, it is physics related, but since it's in pre-calc I put it here.
The problem is I have a plane, it's going N74W, wind is going N20E, the resultant vector is 324mph, and N67W, how do I compensate?

Geometrically: draw the given "resultant vector" at 67 degrees west of north, with "length" 324. Through the tip of that vector, draw a line at angle 74 degrees west of north (continued in both directions and at the initial point of the resultant vector draw a line at angle 20 degrees east of north. That will form a triangle with one side of length 324. Now you have to look carefull at the angles. At the base, the initial point of the you should find that the angle is 67+ (90- 70)= 67+ 20= 87 degrees. At the tip of the resultant vector, the angle inside the triangle is 74- 70= 4 degrees. you can, of course, get the third angle as 180- 87- 4 and then find the lengths by either the sine law or the cosine law.

Homework Equations

I remember going over it once in class but I really don't want to screw it up since this project (which is a lot bigger than just this problem) is supposed to be a big part of the grade.

The Attempt at a Solution

I think I'm just supposed to make a vector go NxW, but I'm not sure how to get it.[/QUOTE]

 

[yamugushi]

Is there a way to do it via component and directional form?