Multi-equation Sin(A+B) help

[DMM_OG]

I have 2 unknowns and 2 equations, but the sin(A+B) is causing me headaches. I know that sin(A+B)=sin(A)cos(B)+sin(B)cos(A), but it has been 20years since college and can't remember how to solve.

X_L=D_B+X_M-[h_B*sin(T_B+A)], and
X_L=D_T+X_M-[h_T*sin(T_T+A)]

I want to solve for X_L, given that A is also an unknown. Also, 0<=A<90deg for my purposes.

Is there an easy solution for X_L?

 

[tkhunny]

If you are solving for X_L, why do you care about the trigonometry information?

It's not real clear what it is you are doing, but I think I would solve BOTH equations for X_M and see if anything else dawns on me.

 

[DMM_OG]

If you are solving for X_L, why do you care about the trigonometry information?

It's not real clear what it is you are doing, but I think I would solve BOTH equations for X_M and see if anything else dawns on me.

My goal is to solve for X_L in which it is not a function of A (since A is unknown). If I could solve for A, then I could substitute that into the other equation and solve for X_L. In the case where T_B and T_T are zero, this simplifies to sin(A) and it is trivial to solve using basic algebra. If T_B and T_T are not zero, I can't figure out how to solve algebraically. Maybe I'm not looking at it the right way, but this is where I'm hoping someone can help.

I've tried to solve the equations by solving each for X_M, but I still end up with a mess of sin(A) and cos(A) and hit a simplification roadblock.