To determine the value of [tex]\(\tan 45^{\circ}\)[/tex], we can analyze the relationship between the angles and their tangents in a right triangle or using trigonometric identities.
1. Understanding Tangent Function:
- The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side:
[tex]\[
\tan \theta = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
2. Applying to [tex]\(\tan 45^\circ\)[/tex]:
- For the angle [tex]\( \theta = 45^\circ \)[/tex] in a right triangle, the opposite and adjacent sides are equal. For example, in an isosceles right triangle, where the two legs are equal in length, both the opposite and adjacent sides to the [tex]\(45^\circ\)[/tex] angle are the same.
3. Evaluate:
- [tex]\(\tan 45^\circ\)[/tex] is thus:
[tex]\[
\tan 45^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{x} = 1
\][/tex]
4. Comparison with Possible Answers:
- We have possible answers:
- A: [tex]\(1\)[/tex]
- B: [tex]\(\frac{1}{2}\)[/tex]
- C: [tex]\(\sqrt{2}\)[/tex]
- D: [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
- Upon analysis, the computed value of [tex]\(\tan 45^\circ\)[/tex] is closest to option A, which is [tex]\(1\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{1}
\][/tex]
