Triangle of Forces

Hi I have a question about three forces in equilibrium. String 1 and String 2, which is at 60 degree and 50 degree to the horizontal is supporting a mass of 500g. We are asked to find tension. I can do it but I use a long method, basically equalling x component to each other and equalling the sum of y components to the weight.

The book's method is really simple but I don't know how they have done it.
They use T1/sin40 = (0.5x9.81)/ (sin110) for T1 and for T2 they use T2/sin50 = (0.5x9.81)/ (sin110). I tried to form a closed triangle but this didn't work.

Thanks!