Answer
$x = \frac{4}{5}$
Work Step by Step
Let $\theta = arctan~\frac{4}{3}$
Then $tan~\theta = \frac{4}{3} = \frac{opp}{adj}$
If the opposite side is 4 and the adjacent side is 3, then the hypotenuse is $\sqrt{4^2+3^2} = 5$
Then $sin~\theta = \frac{4}{5}$
Therefore, $arcsin~\frac{4}{5} = \theta = arctan ~\frac{4}{3}$
$x = \frac{4}{5}$
