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This is a problem involving solving a right triangle, specifically triangle ABC, where:

- \( C = 90^\circ \) (Right angle)
- \( a = 19.1 \, \text{cm} \)
- \( c = 45.7 \, \text{cm} \) (hypotenuse)
- \( b \approx 41.52 \, \text{cm} \)

We are tasked with finding:
- \( b \) (already calculated and provided)
- Angle \( A \) in degrees and minutes.

### Steps:

1. **Calculate Angle \( A \):**
   Use the trigonometric ratio \( \sin(A) = \frac{a}{c} \), since in a right triangle:
   \[
   \sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{a}{c}
   \]

2. **Convert Angle \( A \) to Degrees and Minutes:**
   After finding the angle in decimal degrees, we can convert the decimal part to minutes.

Let me calculate this for you.The angle \( A \) is approximately \( 24^\circ 42' \) (24 degrees and 42 minutes).

Let me know if you'd like more details or further clarifications!

Here are 5 related questions:
1. How do you find angle \( B \) in this triangle?
2. What is the significance of degrees and minutes in angle measurement?
3. How do you convert decimal degrees into minutes?
4. What are some other trigonometric methods to solve for angles in right triangles?
5. Why is the sine function used when the opposite and hypotenuse are known?

**Tip:** In trigonometry, knowing two sides of a right triangle allows you to find any angle using the sine, cosine, or tangent functions depending on which sides you have!

Solve the right triangle ABC, where C = 90°, a = 19.1 cm, and c = 45.7 cm. Find angle A in degrees and minutes and b, rounded to the nearest hundredth.

Learn how to solve a right triangle ABC where C = 90°, a = 19.1 cm, and c = 45.7 cm. Calculate side b and angle A using trigonometric ratios and Pythagoras' theorem, with detailed steps.

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