Answer
$105.2^{\circ}$
Work Step by Step
Given-
$\sin\theta$ = $0.9652$ , $\theta$ belongs to Q II and $0^{\circ}\leq \theta\lt 360^{\circ}$
We will find reference angle of $\theta$ first, using calculator in degree mode by the $\sin^{-1}$ key with the value $0.9652$-
$0.9652$ → $\sin^{-1}$→→ 74.840152956
i.e. reference angle of $\theta$ = $74.8^{\circ}$ (to the nearest tenth of a degree)
The desired angle $\theta$ is in Q II, whose reference angle is $74.8^{\circ}$.
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $180^{\circ} - 74.8^{\circ}$
= $105.2^{\circ}$
