First look only at 



That asks: What angle between 0 and 360 has  for its cosine?

It's a NEGATIVE cosine and the cosine is negative only in QII and QIII.

So it's got to be one of these two:

   

The first one is the PRINCIPLE value, since it has the lesser absolute
value. (The shorter red arc). So we calculate the other side of the triangle 
for the first one, using the Pythagorean theorem:



We choose the positive sign, since it goes up.



That's the picture of



And we want 



Since we know that ,

the answer is

.

Edwin

    You just know that   = .  It is a general formula and general knowledge,
                                                             not depending on the given problem.


    Concretely in the problem, you are given the cosine:  = .

    All you need now, is to calculate   = +/-   and then to take the sign of the sine correctly.

    After that to make the needed ratio and complete simple arithmetic.


        +---------------------------------+
        |    That's all you need to do.   |
        |  That's all they want from you. |
        +---------------------------------+