express tan k as a fraction in simplest terms.

Answer:

$\frac{\sqrt{47}}{17}$

Explanation:

Step1: Recall tangent - ratio formula

$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Identify opposite and adjacent sides to angle $K$

For $\angle K$, opposite side $ML = \sqrt{47}$, adjacent side $LK=17$

Step3: Calculate $\tan K$

$\tan K=\frac{ML}{LK}=\frac{\sqrt{47}}{17}$