Cartesian Vectors: Calculate Magnitude & Direction

[DespicableMe]

Homework Statement

Andrew and David kick a football at the same time. Andrew kicks it with a force 155N and David kicks it with a force 210N. Angle between the two forces is 30 degrees. Calculate the magnitude and direction of the resultant force.

Homework Equations

Cosine law

The Attempt at a Solution

Magnitude = Sqrt (155² + 210² - 2(155)(210)cos30 )
= 108.38N

Direction: Use sine law

I don't understand why the answer at the back of the book used cos 150.

If I were to draw the diagram, would the 2 vectors appear in quadrant 2?

Are they assuming that one of the vectors is parallel to the x axis? (like this):

I was assuming that the vectors were at an angle to the x axis...

 

[LCKurtz]

It doesn't matter what direction they punt in. Look at this picture:

You have figured out r. In the triangle with angle a you know all three sides. If you want to use the law of sines, what angle do you know besides the unknown a? That might answer your question.