Experience the power of community-driven knowledge on IDNLearn.com. Our platform offers reliable and detailed answers, ensuring you have the information you need.

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]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.