Question

find the exact value of \\( \tan q \\) in simplest radical form.

Explanation:

Step1: Recall tangent ratio definition

For angle $Q$, $\tan Q = \frac{\text{opposite side}}{\text{adjacent side}}$

Step2: Identify sides for $\angle Q$

Opposite side to $\angle Q$ is $\sqrt{69}$, adjacent side is $4$.

Step3: Substitute into tangent formula

$\tan Q = \frac{\sqrt{69}}{4}$

Answer:

$\frac{\sqrt{69}}{4}$