In the question, a right triangle with the 3 sides was given.
Considering angle C, the opposite = 30
Adjacent = 16
Hypothenuse = 34
The trigonometric ratio of cos is given by;
![\begin{gathered} \cos \theta=\frac{\text{adjacent}}{\text{hypothenuse}} \\ \cos \text{ C = }(16)/(34) \\ \cos \text{ C = 0.47059} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/ka1f21iq3hpe05c3ak1zp7vqaxceu8lpmz.png)
Therefore, the trigonometrical ratio of cos C to the nearest ten-thousandth is 0.4706