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To solve this problem, we need to determine the value of \(\sin \theta\) for the given triangle.

From the triangle:
- Opposite side = 5
- Hypotenuse = 13

The sine function is defined as:
\[
\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Substituting the values:
\[
\sin \theta = \frac{5}{13}
\]

The correct answer is not in the provided choices. Let me know if you'd like further clarifications or have additional questions! 

Here are some related questions to explore this further:

1. What is the value of \(\cos \theta\) for the given triangle?
2. How do you calculate the adjacent side using the Pythagorean theorem?
3. How can we find the tangent of \(\theta\) using the sides of this triangle?
4. What is the relationship between \(\sin \theta\) and \(\cos \theta\) in terms of trigonometric identities?
5. Can we verify the hypotenuse using the Pythagorean theorem?

**Tip:** Always remember that \(\sin\), \(\cos\), and \(\tan\) values are based on the relationship between specific sides of a right triangle.

Find the value of sin θ for the given right triangle with sides 5, 12, and hypotenuse 13.

Learn how to calculate the sine of angle θ in a right triangle with given sides of 5, 12, and 13 using the sine formula. This trigonometry problem focuses on basic sine function concepts and the Pythagorean theorem, suitable for students in Grades 8-10.

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