To solve for \(\tan 30^{\circ}\), let's consider the trigonometric function \(\tan\), which is defined for an angle \(\theta\) as the ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle.
The value of \(\tan 30^{\circ}\) is a well-known trigonometric identity. Specifically, for an angle of \(30^\circ\):
[tex]\[
\tan 30^\circ = \frac{\sqrt{3}}{3}
\][/tex]
However, this can also be rewritten using a rationalized form:
[tex]\[
\tan 30^\circ = \frac{1}{\sqrt{3}}
\][/tex]
Given the options:
A. \(\sqrt{2}\) \\
B. \(\frac{2}{\sqrt{3}}\) \\
C. \(\frac{1}{\sqrt{3}}\) \\
D. 1 \\
E. \(\frac{\sqrt{3}}{2}\) \\
F. \(\sqrt{3}\)
The correct answer is:
C. \(\frac{1}{\sqrt{3}}\)
Therefore, [tex]\(\tan 30^{\circ} = 0.5773502691896257 \approx \frac{1}{\sqrt{3}} \)[/tex].
