To solve for [tex]\(\tan 60^{\circ}\)[/tex], we need to recall the properties of the tangent function and the values it takes for common angles.
The [tex]\(\tan \theta\)[/tex] function for an angle [tex]\(\theta\)[/tex] in a right triangle is defined as:
[tex]\[
\tan \theta = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
Considering a 60-degree angle in a special 30-60-90 right triangle, the sides have lengths in the ratio [tex]\(1 : \sqrt{3} : 2\)[/tex]. For a 60-degree angle:
- The side opposite the 60-degree angle is [tex]\(\sqrt{3}\)[/tex].
- The side adjacent to the 60-degree angle is [tex]\(1\)[/tex].
- The hypotenuse (tho) is [tex]\(2\)[/tex].
Thus, the tangent of 60 degrees is:
[tex]\[
\tan 60^{\circ} = \frac{\text{side opposite}}{\text{side adjacent}} = \frac{\sqrt{3}}{1} = \sqrt{3}
\][/tex]
This means [tex]\(\tan 60^{\circ}\)[/tex] yields [tex]\(\sqrt{3}\)[/tex].
Comparing this result to the given answer choices:
- A. [tex]\(\sqrt{3}\)[/tex]
- B. [tex]\(\frac{1}{2}\)[/tex]
- C. [tex]\(\frac{2}{\sqrt{3}}\)[/tex]
- D. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
- E. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
- F. 1
We see that the correct answer corresponds to choice A: [tex]\(\sqrt{3}\)[/tex].
Therefore, the answer is:
[tex]\[
A. \sqrt{3}
\][/tex]
