In right triangle $JKL$ with $\angle JLK = 90^\circ$, we have $KL = 8$ and $\tan K = \frac{15}{8}$.  Find $JL$.
To find $JL$, I need to use the relationship between the tangent of an angle and the sides of a right triangle. I recall that $\tan K = \frac{opposite}{adjacent}$, where $opposite$ and $adjacent$ refer to the sides opposite and adjacent to angle $K$, respectively. In this case, the side opposite to $K$ is $JL$ and the side adjacent to $K$ is $KL$. Therefore, I can write $\tan K = \frac{JL}{KL}$ and substitute the given values of $\tan K$ and $KL$. I get $\frac{15}{8} = \frac{JL}{8}$. To isolate $JL$, I can multiply both sides by $8$. I get $JL = \frac{15}{8} \cdot 8 = 15$. 