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To solve for angle \( A \) in the given triangle, we can use trigonometric relationships. The triangle shown is composed of a right triangle and includes angle \( A \), angle \( 30^\circ \), and two sides measuring 3 and 4 units.

### Step-by-step solution:

1. **Use of Sine Law**: We can utilize the sine rule for this type of triangle. In a triangle:
   \[
   \frac{\text{side opposite to angle}}{\sin(\text{angle})} = \frac{\text{side opposite to another angle}}{\sin(\text{another angle})}
   \]
   Since we are given the opposite sides and one angle, we can use this rule effectively.

2. **Right-Angle Considerations**: The triangle can be broken into two right triangles. One part includes the given angle \( 30^\circ \), and we can use trigonometric functions like sine, cosine, or tangent.

To find angle \( A \), we can apply the Law of Cosines or possibly Law of Sines, depending on the relationships between the sides. Let's work through the precise calculation now.The angle \( A \) is approximately \( 22^\circ \) when rounded to the nearest degree.

Do you have any questions or need more details about the solution? Here are some additional related questions:

1. How would the answer change if the side opposite angle \( A \) were longer or shorter?
2. Can you use the Law of Cosines to verify the result?
3. What is the relationship between the sum of angles in a triangle and this result?
4. How does breaking the triangle into two right triangles help in solving similar problems?
5. What other trigonometric functions could be used to find missing angles?

**Tip**: Remember that the sum of angles in any triangle always equals 180°, which can be a useful way to check your work.

Use the information given in the diagram to find A to the nearest degree.

Learn how to find angle A to the nearest degree in a triangle using trigonometric principles such as the Sine Rule and Law of Cosines. This example provides a step-by-step solution suitable for students in Grades 9-11.

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