Are your variables in radiants or degrees? If they are degrees, you had better write your equations this way:

eq1 = (1500 - 100/Sin[alp*Degree])/
    Sin[(180 - alp - th2) Degree] == (Rationalize[1176.795] - 
      100/Tan[alp*Degree])/Sin[th2*Degree];
eq2 = 200 Cos[(90 - alp - th2)*Degree] - 500 Sin[alp*Degree] == 100;

These are trascendental equations, not very suitable for Solve. You can get a feeling for the solutions with a plot

ContourPlot[Evaluate[{eq1, eq2}], {alp, 0, 360}, {th2, 0, 360}]

I can see three probable solution. You can get better approximation with FindRoot