Equilibrium Question With Ropes and Weight

1. The problem statement, all variables and given/known data

Click on photo to enlarge

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

2. Relevant equations

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

3. 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)