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The image shows a trigonometry problem involving a right triangle. The task is to find the value of \(\tan 45^\circ\).

### Solution:

In a right triangle, the tangent of an angle is given by the ratio of the opposite side to the adjacent side:

\[
\tan \theta = \frac{\text{opposite}}{\text{adjacent}}
\]

For \(\theta = 45^\circ\), we have:

\[
\tan 45^\circ = \frac{\text{opposite}}{\text{adjacent}} = 1
\]

This is because, in a 45-degree right triangle, the opposite and adjacent sides are equal, making their ratio equal to 1.

### Answer:

\[
\tan 45^\circ = 1
\]

Would you like more details or have any questions?

### Related Questions:

1. What is the value of \(\tan 30^\circ\)?
2. How does the tangent function relate to the unit circle?
3. What is the general formula for the tangent of an angle in terms of sine and cosine?
4. What are the values of \(\tan\) at \(0^\circ\), \(90^\circ\), and \(180^\circ\)?
5. Can you explain how to derive the tangent values for special angles (30°, 45°, 60°)?

### Tip:
For any angle \(\theta\), \(\tan \theta\) can also be calculated using \(\frac{\sin \theta}{\cos \theta}\).

Learn how to solve the trigonometry problem involving a right triangle to find the value of \(\tan 45^\circ\). Understand the concept of tangent in a right triangle and its application. Suitable for high school students.

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