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 4, and the hypotenuse is $x$.

Step2: Substitute values into formula

$\sin(30^\circ) = \frac{4}{x}$

Step3: Solve for $x$

Since $\sin(30^\circ) = 0.5$, rearrange: $x = \frac{4}{\sin(30^\circ)} = \frac{4}{0.5}$

Step4: Calculate final value

$x = 8.0$

Answer:

$8.0$