Answer
$30.502748^{\circ}$
Work Step by Step
Use the identity $\cos\theta=\frac{1}{\sec\theta}$. If $\sec\theta=1.1606249$, then
$\cos\theta=\frac{1}{1.1606249}$
We can find $\theta$ now by using degree mode and the inverse cosine function.
$\theta=\cos^{-1} (\frac{1}{1.1606249})\approx 30.502748^{\circ}$
