Question

question solve for x. round to the nearest tenth of a degree, if necessary.

Explanation:

Step1: Identify trigonometric ratio

We know that in a right - triangle, $\sin x=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the side opposite to angle $x$ is $24$ and the hypotenuse is $36$. So, $\sin x=\frac{24}{36}=\frac{2}{3}$.

Step2: Solve for $x$

We use the inverse - sine function. $x = \sin^{-1}(\frac{2}{3})$.
Using a calculator, $x=\sin^{-1}(\frac{2}{3})\approx41.8^{\circ}$.

Answer:

$41.8^{\circ}$