Why Does This Statics Problem Not Specify Resultant Force Direction?

[d0ntg3t1t]

Homework Statement

http://imgur.com/a/FyekZ
I took the liberty of uploading everything. The first picture is the question, while the other two is my attempt at answering it in two parts. What I do not understand is what I did wrong or where I went wrong.
I also would like to know why, unlike many other questions from the text, this question does not specify in which direction the resultant force is directed. Is the question wrong, or am I supposed to go about this in a different manner?

EDIT: If you cannot see the full image, please click the gear icon (top right of each image - gear appears when you have the mouse over the image) and select view full resolution.

Homework Equations

See above.

The Attempt at a Solution

Please see above.

 

[CWatters]

Deleted.

 

[CWatters]

Ok so there appears to be too many unknowns unless you assume the resulting force is to be in the "u" direction.

 

[CWatters]

I think you may have made an error in the calc for Fry. Did you forgot to divide by Sin(28)?

 

[CWatters]

Actually it looks like you can calculate the angle of the resultant. Call that β then..

In x..

FR*Cos(β) = F1*Cos(θ) - F2*3/5 + F3*Cos(45)
so
F1*Cos(θ) = FR*Cos(β) + F2*3/5 - F3*Cos(45) ...(1)

In y..

FR*Sin(β) = F1*Sin(θ) + F2*4/5 - F3*Sin(45)
so
F1*Sin(θ) = FR*Sin(β) - F2*4/5 + F3*Sin(45)...(2)


Knowns F2, F3, FR, θ
Unknowns F1 and β

We have two equations and two unknowns.