Answer
$\theta$ = $44.4^{\circ}$
Work Step by Step
Given, $\csc\theta$ = $1.4293$
We will calculate $\sin\theta$ first as calculator does not have $\csc^{-1}$ key.
Using reciprocal identity-
$\sin\theta$ = $\frac{1}{\csc\theta}$ = $\frac{1}{1.4293}$
Using calculator-(1.4293 → $\frac{1}{x}$)
$\sin\theta$ = $0.699643182$
Therefore-
$\theta$ = $\sin^{-1} 0.699643182$
Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI
Using calculator in degree mode-(0.699643182 → $\sin^{-1}$)
$\theta$ = $(44.398383447) ^{\circ}$
On rounding to the nearest tenth of a degree-
$\theta$ = $44.4^{\circ}$
