Can the Law of Sines Determine Chandelier Tension Accurately?

[CandyApples]

Homework Statement

A large chandelier is supported by two ropes. Rope 1 makes a 40 degree angle with the ceiling and has a tension of 150N. Rope two forms a 50 degree angle with the ceiling. What is the tension in rope 2 and what is the mass of the chandelier given the chandelier.

Homework Equations

F = ma
T-mg = ma
Law of sines?

The Attempt at a Solution

So i solved it through the law of sines and got an answer significantly different than what my professor said it should be. I would be interested in knowing why.
Here is the work:
150/sin(50) = T2/sin40
T2 = 150*sin(40)/sin(50)
T2 = 125.86N whereas the correct answer is 179N.

Then for the mass:
150*sin(40)+125.86*sin(50) = mg
m = 19.66kg whereas the correct answer is 23.8kg.

I was wondering why the law of sines did not provide a correct answer in this case, and what different steps I should take to get at the right answer. Thanks in advance!

 

[206PiruBlood]

Is there any particular reason you are using the law of sines? Draw a picture, how can you divide the triangle into two right triangles? Once you do this it is simple right angle trigonometry .

 

[CandyApples]

My apologies, I overcomplicated this problem. Upon drawing a diagram it is obvious Fx = T2cos(50) - 150cos(40). Fy = T2sin50 + 150sin40. Apply second law to Fx and force comes out nicely to 178.8N, plug that into Fy and it is in fact 23.8kg. Thanks for the help :).