Even though your method is the simplest, it assumes that the answer is in the first quadrant, which it might not be. Once the OP has found for in the first quadrant, he/she needs to realise that is also positive in the third quadrant, and in the third quadrant, is negative.
So there are actually two possibilities, the positive and the negative of what the OP finds using your method
Given the level of the question (looks like basic right triangle trig) , I kept the means of solution rather simple. Why make it more difficult for someone who asks for confirmation that their cosine ratio is correct?
I don't really believe the OP is at the level of dealing with trig functions ... yet.