#### Answer

$22.72^{\circ}$

#### Work Step by Step

Ensuring that the calculator is in degree mode, we enter $\sec^{-1} (1.0840880)$ as $\cos^{-1} (\frac{1}{1.0840880})$ into the calculator and solve to the nearest hundred:
$\cos^{-1} (\frac{1}{1.0840880})\approx22.72^{\circ}$