# Finding the magnitude/direction of a resultant vector?

anonymous812

## Homework Statement

Four vectors A, B, C, and D are shown (not to scale). Vector A has magnitude 20.0 and acts at an angle of 12.9 degrees with respect to the positive x axis. Vector B has magnitude 15.0 and acts at an angle of 55.7 degrees with respect to the positive x axis. Vector C has magnitude 31.5 and acts at an angle of 146.5 degrees with respect to the positive x axis. Vector D has magnitude 13.0 and acts at an angle of 296.4 degrees with respect to the positive x axis.

Question: What are the magnitude and direction of the resultant vector, R, when the parallelogram law is applied to A and B?

## Homework Equations

Law of Sines and Law of Cosines..
A/sina=B/sinb=C/sinc
C=sqrt(A^2+B^2-2ABcos(c)

## The Attempt at a Solution

I solved for The resultant vector and got 32.6 N.... R=sqrt(20^2 +15^2-2(20*15*cos(137.2)))
Then I used law of sines to find the direction and got 52.5 degrees.

Apparently, I'm wrong. I recalculated all the angles not given and they seem to be right, but my end result ends up being wrong. Any tips?
Thank you!

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## Answers and Replies

Homework Helper
Gold Member
Then I used law of sines to find the direction and got 52.5 degrees.

You might want to post more detail on what you did here. That's where the problem lies.

anonymous812
Alright, sorry! I did 32.6/sin(r)=15/21.4.
I got 21.4 from the calculating the angle 1/2(ThetaB-ThetaA)

voko
It will be a lot easier to find the components of each vector, then add them component-wise, then find the magnitude and direction of the resultant.

• 1 person
anonymous812
Thanks! You're right that was easier. I got it :)