Start with a Free-Body Diagram of the point where the three ropes meet. I have a +x axis horizontally to the right and a +y axis straight up. There is a tension T1 acting up and to the left making a 35 degree angle with the -x axis, there is a tension T2 acting up and to the right making a 35 degree angle with the +x axis, and there is a weight w acting straight down.

The point we have chosen is stationary and massless. So according to Newton's 2nd in the x-direction:

So we know that . I'm just simply going to refer to this as "T" from now on.

In the y-direction we have:

Thus

I'll let you pick up the rest.

-Dan