Answer
$68.673241^{\circ}$
Work Step by Step
Use the identity $\cos\theta=\frac{1}{\sec\theta}$. If $\sec\theta=2.7496222$, then
$\cos\theta=\frac{1}{2.7496222}$
We can find $\theta$ now by using degree mode and the inverse cosine function.
$\theta=\cos^{-1} (\frac{1}{2.7496222})\approx 68.673241^{\circ}$
