Question

find the side labeled x.
x = 6
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Explanation:

Step1: Recall sine - function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$, the opposite side to the $30^{\circ}$ angle is 3 and the hypotenuse is $x$.
So, $\sin30^{\circ}=\frac{3}{x}$.

Step2: Substitute the value of $\sin30^{\circ}$

We know that $\sin30^{\circ}=\frac{1}{2}$. So, $\frac{1}{2}=\frac{3}{x}$.

Step3: Solve for $x$

Cross - multiply to get $x\times1 = 3\times2$.

Answer:

$x = 6$