Force and tension problems without using Newton's laws

[Shay10825]

Hello. I was trying to find a way to solve the tension problems without using Newton’s laws. The problem says: A weight of 200 kg is supported by two wires. Find the magnitude of the tension in each wire. The angle in the top left is 35 and the angle in the top right is 41.

I used the law of sines and I said that the weight of 200 must be equal to the sum of the two tensions (u and v) which is (u*sin145 + v*sin41)

u/sin49 = (u*sin145 + v*sin41) / sin76

v/sin55 = (u*sin145 + v*sin41) / sin76

But I can’t solve these two equations and I don’t know why. The answer is u = 155.56 and v = 168.486. The answers work with the equation but for some reason I can’t solve these equations ( I keep getting zero).
How can I solve there to equations to get u = 155.56 and v = 168.486?

Also is there another way to solve these problems (without using Newton’s laws) using geometry or some other complicated way. I’m just playing around with the problems and I understand how to solve them using Newton’s laws. I am just curious.

http://img101.imageshack.us/img101/5670/tension2wf.jpg

Thanks

 

[Tide]

You already had the answers when you wrote the law of sines for u and v right after the "so then:" line in your picture.

Also, you are, in fact, using Newton's laws when you wrote your equations. I don't see how you could avoid it.

 

[Shay10825]

I wrote those two equations so you could see where I got the bottom two equations with just the u and v. I wanted to be able to solve the equations:

u/sin49 = (u*sin145 + v*sin41) / sin76

v/sin55 = (u*sin145 + v*sin41) / sin76

so i could solve these problens if they did not give wou the weight of 200.

 

[Shay10825]

so is there any way i can solve the equations:

u/sin49 = (u*sin145 + v*sin41) / sin76

v/sin55 = (u*sin145 + v*sin41) / sin76

for u and v?

 

[Tide]

You should have something like

$$v \sin 39 = u \sin 55$$

and

$$u^2 + v^2 - 2 uv \cos 76 = 200^2$$

and, once again, this is just another expression of Newton's Laws.