Answer
F
Work Step by Step
Recall: $\csc\theta=\frac{1}{\sin\theta}=\frac{\text{hypotenuse}}{\text{opposite side}}$
Given: $x=5\csc 38^{\circ}$
$\implies \csc 38^{\circ}=\frac{x}{5}$
This implies that the hypotenuse is $x$ and the opposite side to the $38^{\circ}$ angle has length $5$. This is the case in the right triangle F.
