Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $\triangle GHI$ with right - angle at $H$, we know the side opposite the $22^{\circ}$ angle ($IH = 96$) and we want to find the hypotenuse $x$. We use the sine function. The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin(22^{\circ})=\frac{IH}{x}$.

Step2: Solve for $x$

We can rewrite the equation $\sin(22^{\circ})=\frac{96}{x}$ as $x=\frac{96}{\sin(22^{\circ})}$.
Since $\sin(22^{\circ})\approx0.3746$, then $x=\frac{96}{0.3746}\approx256.3$.

Answer:

$256.3$