This is a right triangle problem where we need to find the length of side $x$. We are given:

• The hypotenuse $12$,
• One angle $30^\circ$, and
• A right angle $90^\circ$.

Step-by-step Solution:

The side $x$ is opposite the $30^\circ$ angle, and the given hypotenuse is 12. In a right triangle, the sine function relates the opposite side to the hypotenuse:

$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}$

1. Using $\sin(30^\circ)$, we write: $\sin(30^\circ) = \frac{x}{12}$

2. We know $\sin(30^\circ) = 0.5$, so: $0.5 = \frac{x}{12}$

3. Solve for $x$: $x = 12 \times 0.5 = 6$

Final Answer:

The length of $x$ is: $\boxed{6.0}$

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. What trigonometric ratio would you use to find the adjacent side to the $30^\circ$ angle?
2. If the hypotenuse were doubled, how would the value of $x$ change?
3. Can you calculate the length of the side adjacent to the $30^\circ$ angle?
4. How do the angles of a triangle influence the lengths of the sides?
5. How would you use the cosine or tangent function to verify the result?

Tip: Always check the given information carefully to select the correct trigonometric ratio for solving right triangle problems!