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