Question

round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trigonometric relation

In right - triangle $\triangle IJK$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 22^{\circ}$ and the hypotenuse $IK = 16$, and the side opposite to the angle $\theta$ is $x$. So, $\sin(22^{\circ})=\frac{x}{16}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin(22^{\circ})=\frac{x}{16}$ by 16. We get $x = 16\times\sin(22^{\circ})$.
Since $\sin(22^{\circ})\approx0.3746$, then $x = 16\times0.3746=5.9936$.

Step3: Round to nearest tenth

Rounding $5.9936$ to the nearest tenth gives $6.0$.

Answer:

$6.0$