Equilibrium Question With Ropes and Weight

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The problem involves finding the tensions in three ropes supporting a weight of 1000 N. The participant determined that T1 equals 1000 N and that T2 and T3 must sum to 1000 N for equilibrium. They calculated T2 to be 577 N, leading to T3 being 423 N. The discussion emphasizes the importance of analyzing both vertical and horizontal force components at the junction of the ropes. Understanding these components is crucial for solving equilibrium problems involving multiple forces.
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Homework Statement


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The weight at the end of the rope is 1000 N. Find tensions in T1, T2, and T3.

Homework Equations



Law of Cosine: a^2+b^2-2ab(cosC)=c^2
SOH-CAH-TOA

The Attempt at a Solution



T1 has to be 1000N. I figured T2 and T3 have to add up to the weight of 1000 N. I ended up added the vectors head to tail and found T2 to be 577 N and T3 would have to be 1000-577=423 N since both ropes have to add up to 1000 N to be in equilibrium. I honestly do not have a clue how to do the problem (it was on a test today and it's really bugging me what the answer is or how to even achieve the answer)
 
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Consider vertical and horizontal force components. Start by analyzing the vertical forces acting on the junction of the ropes.
 

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