Max Weight for Newton Law Problem Homework

[physstudent1]

Homework Statement

If the maximum tension either rope can sustaine without breaking is 5000N determine the maximum value of the hanging weight that these ropes can safetly support.

the diagram shows two ropes connecting at a node which leads down to a weight,
the first rope on the left is connected to the ceiling making a 60 degree angle with the ceiling and the rope on the left is connected to the ceiling making a 40 degree angle with the ceiling they both converge into one point where a weight hangs.

Homework Equations

The Attempt at a Solution

I drew a free body diagram at the point where the two ropes meet and the weight hangs. And I did 5000*sin60 + 5000*sin40 = maxweight but this is not giving me the correct answer the answer is 6400N. I don't get what I am doing wrong. Here is an attempt at the diagram haha, the angles would be formed on the inside of the V at the top between ceiling and the two sides of the rope.
(V's point to where the angles are)
---V--V-
--\----/---
---\--/----
----\/-----
----|------
---weight---

 

[radou]

Are you sure you got the problem text right? There is something senselsss here - i.e. if you wrote down the equation of equilibrium for the x direction, the resultant would not equal zero, since the angles differ. Equilibrium would only be possible for equal angles.

 

[physstudent1]

well the rope on the 40 angle side appears to be longer but besides that yes everything is correct