What is the weight of block D in this equilibrium of particles problem?

[hdp12]

Homework Statement

Here is the problem that I am stuck on in my mechanics class.

https://lh4.googleusercontent.com/ygXVjNfI4iP8xVpEjhxXZlWlDqg_VrM2gCVFLyomOVwWCfcLU78mIcPEc7hEzUqBoACIiQ=w1210-h506

Homework Equations

F=-kx

The Attempt at a Solution

See the attached picture of my work
https://lh3.googleusercontent.com/dpyJ3aIImPY7kOm33QSuD_bZrqTqVL2DnPjhDp2G0t1wWDM9G5RGHORSXESWWNFp4H7xCfrQrLgu0Y9dzntbhG7AKzM=w1210-h506
I'm so stuck. I don't know what to do from here.

 

[Nathanael]

Why do you think the change in length of spring AB is 3 meters?

P.S.
Just a tip, there's no reason to find the angles spring AB makes; you only care about the sine or cosine of the angles which corresponds to ratios of the sides of the triangle. Finding (and rounding) the angle, like you did, may lead to less accuracy in the final answer.

 

[Nathanael]

Now, about your main problem:

What can you say about the ratio between "F_acx" and "F_acy"?

 

[haruspex]

Why do you think the change in length of spring AB is 3 meters?

Because the unstretched length has been taken as 2m instead of 3m.

 

[hdp12]

What can you say about the ratio between "Facx" and "Facy"

tan(45)=F_ACy/F_ACx or, they're directly proportional bc tan(45) = 1
F_ACy = F_ACx
What do I do with this?

 

[Nathanael]

tan(45)=F_ACy/F_ACx or, they're directly proportional bc tan(45) = 1
F_ACy = F_ACx
What do I do with this?

You calculated F_ACx so now you know F_ACy. You also calculated F_ABy. So what is the weight of block D?

But actually you calculated incorrectly, you'll need to recalculate (but I think you had the right idea). The problem says the unstretched length is 3 meters, not 2 meters.