Provide a simple example of finding the sine ratio of a right triangle

Let's go through a simple example to find the sine ratio of a right triangle.

### Example:
Consider a right triangle with the following sides:
- **Opposite side** (to the angle \(\theta\)) = 3 units
- **Hypotenuse** = 5 units

### Step-by-Step Solution:

1. **Identify the sides relative to the angle \(\theta\)**:
   - The **opposite side** is the side opposite the angle \(\theta\).
   - The **hypotenuse** is the longest side of the triangle, opposite the right angle.

2. **Use the sine ratio formula**:
   \[
   \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}
   \]

3. **Substitute the values**:
   \[
   \sin(\theta) = \frac{3}{5}
   \]

4. **Simplify the fraction**:
   \[
   \sin(\theta) = 0.6
   \]

### Conclusion:
The sine of the angle \(\theta\) in this right triangle is \(0.6\).

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Would you like to explore further details or have any questions?

### Related Questions:
1. How would you find the cosine ratio of the same triangle?
2. How do you find the length of the opposite side if you know \(\sin(\theta)\) and the hypotenuse?
3. What is the sine ratio for a 45-degree angle in a right triangle?
4. How can you verify that your sine ratio is correct?
5. How do you find the angle \(\theta\) if you only know \(\sin(\theta) = 0.6\)?

### Tip:
When dealing with trigonometric ratios, make sure the triangle is a right triangle (one angle is 90 degrees).

Explore how to find the sine ratio of a right triangle with a detailed step-by-step example. Understand the sine ratio formula and apply it to calculate the sine of an angle in a right triangle. Suitable for Grades 9-12.

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