Object suspended by two cables, what are the tensions of each cable?

[amyo16]

Homework Statement

Consider there is a 634 N weight held by two cables that meet at a point above the weight. The left cable with tension T sub 2 makes an angle of 46° to the horizontal. The right cable with tension T sub 1 makes an angle of 40° to the horizontal.
a) What is the tension in the cable labeled T sub 1 slanted at an angle of 40°?
b) What is the tension in the cabel labeled T sub 2 slanted at an angle of 46°?

Homework Equations

I feel that the only relevant equation in this case is that the Tension always equals the Force. Therefore F sub T would equal the weight.

The Attempt at a Solution

I attempted to logically conclude that by splitting each tension force into components, the x components of each would have to equal 0 to balance each other out. I also thought that the y components of each would have to be equal to each other since they are the same height. So I had the equations Tsub1xsin40+Tsub2xsin46=634. I also had that Tsub1xcos40-Tsub2xcos46=0. Then I solved the second equation for Tsub1 and plugged it into the first equation and solved, but the answer was wrong. Help?

 

[ehild]

Hi amyo16, wwelcome to PF.
Your method and equations are correct, (except the sentence

the y components of each would have to be equal to each other since they are the same height

which is not true). You might have miscalculated something, show your numerical results.

ehild