Remember the definitions of the trigonometric ratios on a right triangle:
[tex]\sin (A)=\frac{\text{Side opposed to A}}{Hypotenuse}[/tex][tex]\cos (A)=\frac{\text{Side adjacent to A}}{\text{ Hypotenuse}}[/tex][tex]\tan (A)=\frac{\text{Side opposed to A}}{\text{ Side adjacent to A}}[/tex]Then, from the given information on the diagram:
[tex]\begin{gathered} \sin A=\frac{36}{45}=\frac{4}{5} \\ \cos A=\frac{27}{45}=\frac{3}{5} \\ \cos C=\frac{36}{45}=\frac{4}{5} \\ \tan C=\frac{27}{36}=\frac{3}{4} \end{gathered}[/tex]