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To find the value of \(\sin(\alpha)\), we need to determine the ratio of the opposite side to the hypotenuse in the given right triangle.

Given:
- Opposite side to angle \(\alpha\): \(5\)
- Hypotenuse: \(6.5\)

The formula for \(\sin(\alpha)\) is:

\[
\sin(\alpha) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{5}{6.5}
\]

Now, let's compute this value:

\[
\sin(\alpha) \approx \frac{5}{6.5} \approx 0.769
\]

So, \(\sin(\alpha) \approx 0.769\).

Would you like a more detailed explanation, or do you have any other questions?

### Related Questions:
1. What is the value of \(\cos(\alpha)\)?
2. How do you calculate the length of the remaining side using the Pythagorean theorem?
3. What is the value of \(\sin(\theta)\) in this triangle?
4. How do you find the angle \(\alpha\) using \(\sin(\alpha)\)?
5. What are the properties of a right triangle?

### Tip:
In a right triangle, the sine, cosine, and tangent functions can be easily remembered using the mnemonic "SOH-CAH-TOA."

Learn how to find the value of sin(⍺) for a right triangle with an opposite side of 5 and a hypotenuse of 6.5. This step-by-step guide covers the key trigonometric concepts, including the sine formula and the Pythagorean theorem. Suitable for students in Grades 8-10.

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