Using vectors to calculate tension.

[-Dragoon-]

Alright, so this question was giving me problems and I made one up to solve for practice, but I have no way to check if I did it correctly, so I would appreciate if you could I did it correctly.

Homework Statement

A 150N chandelier is suspended from a ceiling at a single point by two chains that make angles of 25° and 30° with the ceiling. Calculate the tension on each chain.

Homework Equations

$$T_{1}\cos{25} = T_{2}\cos{30}$$
$$T_{1}\sin{25} + T_{2}\sin{30} = 150 N$$

The Attempt at a Solution

First, I'll label the chain that makes an angle of 25° with the ceiling be T_1 and the chain that makes an angle of 30° with the ceiling be T_2
First I decide to solve for T_2 by using the first equation:
$$T_{1}\cos{25} = T_{2}\cos{30}$$
$$T_{2} = \frac{T_{1}\cos{25}}{\cos{30}}$$
$$T_{2} = 1.05T_{1}$$
Now I substitute this into the second equation:
$$T_{1}\sin{25} + 1.05T_{1}\sin{30} = 150 N$$
$$0.423T_{1} + 0.525T_{1} = 150$$
After doing simple algebra, I yield:
$$T_{1} \approx 158.23 N$$
Now to substitute this to find the tension of the other chain:
$$T_{2} = 1.05(158.23N) => T_{2} \approx 166.14 N$$

Therefore, the tensions in the two chains are approximately 166.14 N and 158.23 N. Did I do this correctly? Thanks in advance. Also, what would be an efficient way of checking my solution is correct?

 

[Quinzio]

It's correct.
No way of simple checking. The problem is simple itself :)

 

[-Dragoon-]

It's correct.
No way of simple checking. The problem is simple itself :)

Thank you for the help.