Question

express tan $k$ as a fraction in simplest terms.
answer
$\tan k = $

Explanation:

Step1: Recall tangent ratio definition

For an acute angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$

Step2: Identify sides for $\angle K$

Opposite side to $\angle K$: $\sqrt{47}$, Adjacent side to $\angle K$: $17$

Step3: Substitute into tangent formula

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

Answer:

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