Answer:
The value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]
Explanation:
Given the triangle in the attached image.
Recall that;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]
from the given figure;
[tex]\begin{gathered} \theta=30^{\circ} \\ \text{opposite}=f \\ \text{adjacent}=3\sqrt[]{6} \end{gathered}[/tex]
substituting the values;
[tex]\begin{gathered} \tan 30=\frac{f}{3\sqrt[]{6}} \\ f=3\sqrt[]{6}\tan 30 \\ f=3\sqrt[]{6}(\frac{\sqrt[]{3}}{3}) \\ f=3\sqrt[]{2} \end{gathered}[/tex]
Therefore, the value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]
