Answer
$\theta$ = $33.3^{\circ}$
Work Step by Step
Given, $\csc\theta$ = $1.8214$
We will calculate $\sin\theta$ first as calculator does not have $\csc^{-1}$ key.
Using reciprocal identity-
$\sin\theta$ = $\frac{1}{\csc\theta}$ = $\frac{1}{1.8214}$
Using calculator-(1.8214 → $\frac{1}{x}$)
$\sin\theta$ = $0.5490282201$
Therefore-
$\theta$ = $\sin^{-1} 0.5490282201$
Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI
Using calculator in degree mode-(0.5490282201 → $\sin^{-1}$)
$\theta$ = $(33.300370319) ^{\circ}$
On rounding to the nearest tenth of a degree-
$\theta$ = $33.3^{\circ}$
