Solution:

We divide this problem into two parts, one for each junction: The first, and easiest one is the junction between the block and cable 3:

Since there are no horizontal components here life is fairly easy, in order for ,

Now look at the other junction, where all 3 cables are connected together:

Here you need to divide things up into components -- making sure both x and y components of the tension (force) add up to zero.

Add up the x components:

Then the y components:

So now we have two equations with two unknowns. The easy way to do this is solve for in the x component equation, and plug it into the y component equation...

Then you plug this into one of the other equations:

So, the tensions are: