# Vector problem; using undefined values (2D)

1. Sep 14, 2007

### Vidatu

1. The problem statement, all variables and given/known data

2. Relevant equations

sine law : (A)/(sin a) = (B)/(sin b) = (C)/(sin c)
cosine law : c^2 = ( (a^2) + (b^2) - (a)(b)(cos A)
vector addition : R^2 = (Rx)^2 + (Ry)^2
= ((Ax + Bx +Cx)i )^2 + ((Ay + By + Cy)j )^2

3. The attempt at a solution

Well, I'm completely stumped as to how to finish this, or even if I'm on the right track. Any one able to help?

2. Sep 14, 2007

### rootX

yours that sin 60 + 2/3 sin 30 .. is wrong!
because f1 is acting upwards, and other two downward.

and otherwise everything else looks good.

once you find theta, just substitute its value in any of those above equations, and you get F.

3. Sep 14, 2007

### Vidatu

Wow, can't believe I missed that....

Oh well, I fixed it. However, I still have a problem. I get:

n sin (theta) = 1.077
n cos (theta) = 0.5327
theta = 63.69

n should be equal for those two equations, yes? Yet it isn't. Did I mess up somewhere else?

4. Sep 14, 2007

### rootX

n = 1.077 / sin (63.69)
n = 0.5327 / cos(63.69)

and isn't it equal?

5. Sep 14, 2007

### Vidatu

Wow, I'm slow tonight.

When I typed in those values before, I got them reversed. Thus:

n sin (theta) = 0.5327
n cos (theta) = 1.077
theta = 63.69

This might seem that I still have a problem, right? But i figured it out. In my calculations, I wasn't finding theta, I was finding the angle between theta and the negative x axis. So I can either replace "theta" with "90 - theta", or switch my "n sin (theta)"s to "n cos (theta)"s, and vice versa.

Wow, I feel dumb today. Two very simple mistakes, which took me so long to work out.

Anyway, thanks for the help.

Last edited: Sep 15, 2007