https://file.aiquickdraw.com/mathbot/file/172670588949137g6lcak.jpg

The image depicts a right triangle \( \triangle ABC \) with a right angle at \( B \). The sides are labeled as follows:

- \( AB = 24 \)
- \( BC = 32 \)
- \( AC = 40 \)

We are asked to find \( \sin A \).

In a right triangle, the sine of an angle is defined as:

\[
\sin A = \frac{\text{opposite}}{\text{hypotenuse}}
\]

For angle \( A \):

- The side opposite to \( A \) is \( BC = 32 \).
- The hypotenuse is \( AC = 40 \).

Thus,

\[
\sin A = \frac{BC}{AC} = \frac{32}{40} = 0.8
\]

Therefore, \( \sin A = 0.8 \).

Would you like more details or have any further questions?

Here are 5 related questions to explore further:

1. What is \( \cos A \) for this triangle?
2. How would you calculate \( \tan A \) for this triangle?
3. Can you find \( \sin C \) for this triangle?
4. How can you verify the Pythagorean theorem with these side lengths?
5. How does knowing the sine of an angle help in solving real-world problems?

**Tip:** In right triangles, trigonometric ratios like sine and cosine help in relating angles to side lengths, which can be very useful in practical applications like navigation or construction.

Find \( \sin A \) for the right triangle with sides \( AB = 24 \), \( BC = 32 \), and \( AC = 40 \).

Learn how to calculate \( \sin A \) for a right triangle with sides \( AB = 24 \), \( BC = 32 \), and \( AC = 40 \). This problem covers key trigonometric concepts and the Pythagorean Theorem, suitable for students in Grades 9-10.

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