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Find [tex]\tan 30^{\circ}[/tex].

A. [tex]\frac{1}{2}[/tex]
B. [tex]\frac{\sqrt{3}}{3}[/tex]
C. [tex]\sqrt{5}[/tex]


Sagot :

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]
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