When solving for the lengths of the sides of a right triangle, we can make use of the acronym SOH-CAH-TOA. In this problem, because x is adjacent to the 52-degree angle and we are also given the length of the hypotenuse, we can use the "CAH" part, which stands for cosine x = adjacent/hypotenuse.
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \\ \cos52=\frac{x}{18} \\ \\ 18\cos52=x \\ \\ 11.08=x \end{gathered}[/tex]So the answer is x = 11.08.
