Question 1 of 10

What is [tex]$\tan 30^{\circ}$[/tex]?

A. [tex]\sqrt{2}[/tex]

B. [tex]\frac{2}{\sqrt{3}}[/tex]

C. [tex]\frac{1}{\sqrt{3}}[/tex]

D. 1

E. [tex]\frac{\sqrt{3}}{2}[/tex]

F. [tex]\sqrt{3}[/tex]



Answer :

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].