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The image shows a mathematical problem related to trigonometry and triangle geometry. Here's the problem as interpreted from the image:

### Problem Statement:
You are asked to prove the trigonometric identity:

\[
\frac{\sin(\angle BAC)}{\sin(\angle ABC)} = \frac{AC}{AB}
\]

In the context of a triangle \(ABC\), the problem also involves using the Sine Rule (or Law of Sines), which states that for any triangle:

\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]

### Solution:

To prove the identity \(\frac{\sin(\angle BAC)}{\sin(\angle ABC)} = \frac{AC}{AB}\):

1. **Apply the Law of Sines in Triangle \(ABC\)**:
   - According to the Law of Sines:
     \[
     \frac{AB}{\sin(\angle ACB)} = \frac{AC}{\sin(\angle ABC)} = \frac{BC}{\sin(\angle BAC)}
     \]
   
   - Isolate the ratios involving \(AB\) and \(AC\):
     \[
     \frac{AC}{\sin(\angle ABC)} = \frac{AB}{\sin(\angle ACB)}
     \]

2. **Express \(\sin(\angle ACB)\) in terms of the others**:
   - From the above, rearrange to get:
     \[
     \frac{\sin(\angle BAC)}{\sin(\angle ABC)} = \frac{AC \cdot \sin(\angle ACB)}{AB \cdot \sin(\angle ACB)} = \frac{AC}{AB}
     \]
   
3. **Conclusion**:
   - The identity is proven: 
     \[
     \frac{\sin(\angle BAC)}{\sin(\angle ABC)} = \frac{AC}{AB}
     \]
  
This conclusion follows directly from the Law of Sines, confirming that the identity holds true.

Would you like more details on this solution or have any further questions? 

### Related Questions:
1. How is the Law of Sines derived from the properties of a triangle?
2. Can the Law of Cosines be applied to solve similar problems?
3. What are the implications of this identity in solving triangle-related problems?
4. How does this identity relate to the concept of similar triangles?
5. Can this identity be used to find the unknown sides or angles of a triangle in real-world applications?

### Tip:
When working with trigonometric identities in triangles, always consider applying the Law of Sines or Law of Cosines to simplify and verify the relationships between angles and sides.

Learn how to prove the trigonometric identity sin(BAC) / sin(ABC) = AC / AB using the Law of Sines. This problem involves triangle geometry and trigonometric principles, suitable for high school students.

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