Question

find the length of side x to the nearest tenth.

Explanation:

Step1: Identify trigonometric ratio

We use the sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For the $30^\circ$ angle, the opposite side is 11, and the hypotenuse is $x$.
$\sin(30^\circ) = \frac{11}{x}$

Step2: Solve for $x$

Rearrange the formula to isolate $x$: $x = \frac{11}{\sin(30^\circ)}$
We know $\sin(30^\circ) = 0.5$, so substitute:
$x = \frac{11}{0.5} = 22.0$

Answer:

22.0