Since they are similar triangles then their corresponding angles are equal. So, you have
[tex]\begin{gathered} m\angle K=m\angle R \\ m\angle J=m\angle S \\ m\angle L=m\angle Q \end{gathered}[/tex]
Therefore, the value of tan(S) to the thousandths place will be
[tex]\begin{gathered} \tan (S)=\tan (25\text{\degree}) \\ \tan (S)=0.466 \end{gathered}[/tex]
