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To solve for \( \sin(\theta) \) based on the given right triangle:

1. **Identify the sides**: In the triangle,
   - The opposite side to \( \theta \) is 4.
   - The adjacent side is 3.
   - The hypotenuse is 5.

2. **Apply the sine function**: 
   \[
   \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{4}{5}
   \]

So, \( \sin(\theta) = \frac{4}{5} \) or 0.8 in decimal form.

It seems like the answer "45" shown in the image may be incorrect or related to a different question. Would you like more details or clarification?

Here are five related questions to further your understanding:
1. What is \( \cos(\theta) \) for the same triangle?
2. How is \( \tan(\theta) \) calculated using this triangle?
3. Can we use the Pythagorean theorem to verify the lengths of the sides?
4. What are the values of \( \sin(90^\circ - \theta) \) and \( \cos(\theta) \)?
5. How do sine and cosine functions relate in the unit circle?

**Tip:** Remember the acronym **SOH-CAH-TOA** to easily recall trigonometric ratios.

Learn how to calculate sin(θ) for a right triangle with sides 3, 4, and 5. This example applies basic trigonometry concepts such as the sine function and the Pythagorean theorem. Ideal for students in Grades 8-10.

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