1. Let's solve a problem involving trigonometry. 2. Suppose we want to find the value of $\sin(30^\circ)$. 3. The formula for sine in a right triangle is $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. 4. Important rule: $\sin(30^\circ) = \frac{1}{2}$, which is a standard value from the unit circle. 5. Therefore, $\sin(30^\circ) = \frac{1}{2}$. 6. This means the length of the side opposite the 30-degree angle is half the length of the hypotenuse in a right triangle. Final answer: $\sin(30^\circ) = \frac{1}{2}$.