How Do I Derive the Equation for Theta in a Tension Problem?

[narsasistickx]

I have a conceptual problem i can't seem to understand how to derive an equation for theta. Here is what i have so far


Diamgram: L=50m (delta) Y= .20m
A bird sits on a wire whos length is = to 50m the bird acts on the wire and (delta) Y= -.20m. Assuming the bird rests in the middle of the wire, find (theta) and total tension. (Ft)
First equation used. VISUAL |--------O---------|
Its hard to tell by the diagram i created but the bird breaks the wire into components of X and y, so its basically a Vector problem to solve for Theta but i would like to know how to derive to actually solving for theta that would be helpfull. I give an example below as to what i need help with.
Solve for Ft and Theta (which in the diagram is the angle left of the bird or (O) at which it sits.
Example:
(Sigma)F=MA
Which i then reform to Ft=(MG/2sine)
by setting Fy=O FtLy+FtRy+mg(y)=0
Ftsin+Ftrsin=mg
2Ftsin=MG
solve for FT
Ft=(mg/2sin)
is my final equation to solve for Ft

Now that that's how far i have gotten. What i need to know is how do i derive an equation for Theta. I have no freaking clue :D

 

[rootX]

you want theta?

Then, just use simply trignometry

tan theta = y/x