What is the Law of Cosines for Calculating Vector Magnitudes?

[Andy111]

Homework Statement

Consider two vectors ~A and ~B and their resul-
tant ~A + ~B . The magnitudes of the vectors ~A
and ~B are, respectively, 12.1 and 7 and they
act at 130◦ to each other.

Use the law of cosines to calculate the mag-
nitude of the resultant vector ~A + ~B.

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Homework Statement

Consider two vectors ~A and ~B and their resul-
tant ~A + ~B . The magnitudes of the vectors ~A
and ~B are, respectively, 12.1 and 7 and they
act at 130◦ to each other.

Use the law of cosines to calculate the mag-
nitude of the resultant vector ~A + ~B.

Homework Equations

The Attempt at a Solution

How do you figure to apply the Law of Cosines?

 

[Andy111]

I did (A+B)$$^{2}$$=A$$^{2}$$+B$$^{2}$$-2ABcos(130) and solved for (A+B). I got an answer of 17.444148, but that was wrong.

 

[Redbelly98]

Draw a triangle using those vectors.

edit:
This will show you the angle you are supposed to use for the calculation.

 

[Andy111]

I'm a bit lost, why isn't 130 the correct angle to use?

 

[Redbelly98]

Did you draw the triangle?

A picture is worth 1000 words.

 

[Andy111]

Well yes, and I put the angle 130 between A and B, and if that's correct then I don't know how I got this wrong.

 

[Redbelly98]

The correct picture is the 2nd one here.

 

[Andy111]

Thanks, I see where my mistake was now, I didn't draw the vectors "tip-to-tail".