IDNLearn.com makes it easy to find accurate answers to your specific questions. Join our Q&A platform to access reliable and detailed answers from experts in various fields.
Sagot :
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]
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]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.