Tension of rope between two trees

[PhizKid]

Homework Statement

Homework Equations

F = ma

The Attempt at a Solution

say I project the weight onto T
then I get the right answer
if theta = pi / 4 then Wcostheta = W / sqrt2
but if I project the tension onto the weight, i don't get the right thing
i get the opposite, Tcostheta = W
which makes no sense
i guess the question is
is Wcostheta - T = 0
or is Tcostheta - W = 0?
which forces actually balance out
im trying to see what balances out
i mean its really intuitively obvious that Tcostheta - W = 0 should be true
but that doesn't give the right answer
its not accelerating vertically so Tcostheta - W = 0 should be true
weird that it isnt
i don't think weight is just W there

 

[gneill]

Two trees are supporting the weight of the rope. What does that tell you about the vertical component of the tension at each end? What then is the tension?

At the midpoint of the rope only horizontal forces are acting in tension. The trees are providing the horizontal reaction force (equal and opposite, so nothing is moving). What's the horizontal component of the tension found above?

 

[PhizKid]

Nvm, it's because I forgot to divide by 2