I've been struggling with the followings equations (I know that can be solved by Trig. identities method) and I tried almost everything but I can't get them right.

the equations are the following:

-Tab*cos(alpha)+Tbc*cos(beta) = 0 (eq.1)

Tab*sin(alpha)+Tbc*sin(beta)=15

We know the angular values for alpha and beta, and also I reviewed the answers on my workbook and they are; Tab=9.67 and Tbc=12.334, I would like if someone can show me how to solve those identities step by a step.

Thanks in advance

Those equations are part of a problem in mechanics of materials, in which two wires are supporting a weigth (15) both in different known angles (that's why the equations of equilibrium yield those two precedent equations) but I can't get the correct results for each tension in the wires, I know they are trig. identities and something I am doing is not coming well enough in the algebraic procedure.

Thanks