Solve usually works best with polynomial problems. Reduce can often do better with trig problems.

Since you included 180 and 90 in your trig functions I assume you might be thinking in degrees rather than radians. So I inserted a couple of Degree. You may need to insert more of those is you are thinking some of your other constants are in degrees. When you get the solution you can then divide each of the numeric values by Degree to get from radians back to degrees. Look at Degree in the help system for more information.

Since you have two equations and two unknowns and trig functions there is more than one solution. Some of those additional solutions depend on multiples of pi and those multiples are indicated by unknown constants C[1] and C[2]. There are even some solutions involving complex numbers, which you might not be interested in.

eq1 = (1500 - 100/Sin[alp])/Sin[180 Degree - alp - th2] == (1176.795 - 100/Tan[alp])/Sin[th2];
eq2 = 200 Cos[90 Degree - alp - th2] - 500 Sin[alp] == 100;
Reduce[{eq1, eq2}, alp]