Answer
$101.26735^{\circ}$
Work Step by Step
Ensuring that the calculator is in degree mode, we enter $\sec^{-1} (-5.1180378)$ as $\cos^{-1} (\frac{1}{-5.1180378})$ into the calculator and solve:
$\cos^{-1} (\frac{1}{-2.7733744})\approx101.26735^{\circ}$
