solve for x.\nround to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

We know the opposite side ($9$ cm) and the hypotenuse ($17$ cm) of the right - triangle with respect to angle $x$. We use the sine function, $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$. $\sin(x)=\frac{9}{17}$

Step2: Solve for $x$

Take the inverse - sine of both sides. $x = \sin^{-1}(\frac{9}{17})$. $x=\sin^{-1}(\frac{9}{17})\approx31.97^{\circ}$ (using a calculator and rounding to the nearest hundredth)

Answer:

$31.97$