Question

find the exact value of tan g in simplest radical form.

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle G$, the opposite side to $\angle G$ is $EF$ and the adjacent side is $FG$.

Step2: Identify side lengths

We are given that $EF = \sqrt{66}$ and $FG = 5$.

Step3: Calculate $\tan G$

$\tan G=\frac{EF}{FG}=\frac{\sqrt{66}}{5}$

Answer:

$\frac{\sqrt{66}}{5}$