solve for x. round to the nearest tenth, if necessary. answer attempt 1 out of 3 x =

Explanation:

Step1: Identify trig - ratio

In right - triangle $\triangle PQR$ with right - angle at $Q$, we know the side opposite the angle $19^{\circ}$ is $7.6$ and we want to find the hypotenuse $x$. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin(19^{\circ})=\frac{7.6}{x}$.

Step2: Solve for $x$

Cross - multiply to get $x\sin(19^{\circ}) = 7.6$. Then $x=\frac{7.6}{\sin(19^{\circ})}$.

Step3: Calculate the value

We know that $\sin(19^{\circ})\approx0.326$. So, $x=\frac{7.6}{0.326}\approx23.3$.

Answer:

$23.3$