Question

Find f.Write your answer in simplest radical form. ___ units

Answer 1

The value of f is;

`f=3\sqrt[]{2}\text{ units}`

Step-by-step explanation:

Given the triangle in the attached image.

Recall that;

`\tan \theta=(opposite)/(adjacent)`

from the given figure;

`\begin{gathered} \theta=30^(\circ) \\ \text{opposite}=f \\ \text{adjacent}=3\sqrt[]{6} \end{gathered}`

substituting the values;

`\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}`

Therefore, the value of f is;

`f=3\sqrt[]{2}\text{ units}`