https://file.aiquickdraw.com/mathbot/file/17254856105821f3t7diq.png

To find \(\sin(\alpha)\) in the given triangle, we can use the definition of the sine function in a right triangle:

\[
\sin(\alpha) = \frac{\text{opposite side}}{\text{hypotenuse}}
\]

Here, \(\alpha\) is the angle at vertex \(A\), and the opposite side is \(20\) (side \(BC\)). The hypotenuse is the side \(AB\), which is given as \(29\).

So, the sine of \(\alpha\) is:

\[
\sin(\alpha) = \frac{20}{29}
\]

Thus, \(\sin(\alpha) = \frac{20}{29}\).

Would you like more details or have any further questions?

### Related Questions:
1. How do you calculate the cosine of angle \(\alpha\) in this triangle?
2. What is the tangent of angle \(\alpha\)?
3. How can you find the angle \(\alpha\) using inverse trigonometric functions?
4. Can you verify if this triangle is a right triangle using the Pythagorean theorem?
5. How would you find the area of this triangle?

### Tip:
When working with right triangles, always remember that the hypotenuse is the longest side and is opposite the right angle.

Learn how to find the sine of angle \(\alpha\) in a right triangle with sides 20, 21, and hypotenuse 29. This problem covers essential trigonometric concepts and the use of sine function in right triangles, suitable for students in Grades 9-10.

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