What is cos (x)? for the image below?

To find cos x, we must first find sin x.  sin x = opp / hyp = 32/58.

Note the identity (sin x)^2 + (cos x)^2 = 1.  Since we want cos x, solve this for 

(cos x)^2:   (cos x)^2 = 1 - (sin x)^2.

Here,          (cos x)^2 = 1 - (32/58)^2 = 
                        
                      
However, it'd be much easier to find the length of the 3rd side using the Pythagorean Theorem:

58^2 = 32^2 - x^2   =>  2340 = x^2     and x = +48.37.

If we round this off, we get cos x = adj / hyp = 48/58.  This is Answer A.