Since this is a right triangle, we can use our trigonometric functions to solve for x.
Since we know the adjacent side and hypotenuse, we will use cosine.
Based on the function [tex]\cos(x) = \frac{adj}{hyp}[/tex], we can solve for x. The adjacent side is 7 and the hypotenuse is 12. Plugging this in, we get [tex]\cos(x) = \frac{7}{12}[/tex].
Now, we must use our inverse trigonometric functions to solve for x:
[tex]\cos^{-1}(\cos(x)) = \cos^{-1}(\frac{7}{12})[/tex]
The inverse cosine and cosine on the left side cancel, leaving you with:
[tex]x = \cos^{-1}(\frac{7}{12}) = \boxed{54.3^{\circ}}[/tex]
