Answer
$\theta$ = $65^{\circ}43'$
Work Step by Step
Given, $\cos\theta$ = $0.4112$
Therefore-
$\theta$ = $\cos^{-1} 0.4112$
Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI
Using calculator in degree mode-(0.4112 → $\cos^{-1}$)
$\theta$ = $(65.719760758) ^{\circ}$
$\theta$ = $65^{\circ} + (0.719760758)^{\circ}$
$\theta$ = $65^{\circ} +( 0.719760758\times60)'$
(Recall $1^{\circ}$ = $60'$)
$\theta$ = $65^{\circ} +43'$ (Rounding to the nearest minute)
$\theta$ = $65^{\circ}43'$
