Answer
$\theta$ = $84^{\circ}30'$
Work Step by Step
Given, $\sin\theta$ = $0.9954$
Therefore-
$\theta$ = $\sin^{-1} 0.9954$
Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI
Using calculator in degree mode-(0.9954 → $\sin^{-1}$)
$\theta$ = $(84.502273052) ^{\circ}$
$\theta$ = $84^{\circ} + (0.502273052)^{\circ}$
$\theta$ = $84^{\circ} +( 0.502273052\times60)'$
(Recall $1^{\circ}$ = $60'$)
$\theta$ = $84^{\circ} +30'$ (Rounding to the nearest minute)
$\theta$ = $84^{\circ}30'$
