find x. round your answer to the nearest tenth of a degree.

Explanation:

Step1: Identify trig - function

We know that $\sin x=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the opposite side to angle $x$ is $8$ and the hypotenuse is $14$. So, $\sin x=\frac{8}{14}=\frac{4}{7}$.

Step2: Solve for $x$

Using the inverse - sine function, $x = \sin^{-1}(\frac{4}{7})$.

Step3: Calculate the value

$x=\sin^{-1}(\frac{4}{7})\approx34.8^{\circ}$ (using a calculator).

Answer:

$34.8$