To determine the value of [tex]\(\tan 30^{\circ}\)[/tex], we should use the known values of standard angles in trigonometry.
Firstly, let's recall the basic trigonometric values for standard angles. For [tex]\(\tan 30^{\circ}\)[/tex], it is well-known that:
[tex]\[
\tan 30^{\circ} = \frac{1}{\sqrt{3}}
\][/tex]
To simplify [tex]\(\frac{1}{\sqrt{3}}\)[/tex], we rationalize the denominator:
[tex]\[
\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}
\][/tex]
So, [tex]\(\tan 30^{\circ} = \frac{\sqrt{3}}{3}\)[/tex].
Given the options:
- A. [tex]\(\frac{1}{2}\)[/tex]
- B. [tex]\(\frac{\sqrt{3}}{3}\)[/tex]
- C. [tex]\(\sqrt{5}\)[/tex]
We can see that the correct answer is option B, [tex]\(\frac{\sqrt{3}}{3}\)[/tex]. Therefore, the correct choice to [tex]\(\tan 30^{\circ}\)[/tex] from the given options is:
B. [tex]\(\frac{\sqrt{3}}{3}\)[/tex]
