To find $\sin \theta$, where $\theta$ is the given angle in the right triangle, we use the definition of sine in terms of a right triangle:

$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$

In the triangle provided:

• The length of the side opposite $\theta$ is $3$.
• The length of the hypotenuse is $5$.

Thus,

$\sin \theta = \frac{3}{5}$

So, the exact value for $\sin \theta$ is $\frac{3}{5}$.

Would you like further details, or do you have any other questions?

Here are some related questions for further exploration:

1. What is the cosine of $\theta$ in this triangle?
2. What is the tangent of $\theta$ in this triangle?
3. How can we verify if this triangle is a 3-4-5 triangle?
4. How do we find $\cos \theta$ and $\tan \theta$ using exact values?
5. What is the Pythagorean identity and how does it relate to this triangle?

Tip: Remember, in a right triangle, the hypotenuse is always the longest side, and it is opposite the right angle.