Answer
$210.5^{\circ}$
Work Step by Step
Given-
$\tan\theta$ = $0.5890$ , $\theta$ belongs to Q III
We will find reference angle of $\theta$ first, using calculator in degree mode by the $\tan^{-1}$ key with the positive value $0.5890$-
$0.5890$ → $\tan^{-1}$→→ 30.498085114
i.e. reference angle of $\theta$ = $30.5^{\circ}$ (to the nearest tenth of a degree)
The desired angle $\theta$ is in Q III, whose reference angle is $30.5^{\circ}$.
Also $0^{\circ}\leq \theta\lt 360^{\circ}$ Therefore-
$\theta$ = $ 180^{\circ} + 30.5^{\circ}$
= $210.5^{\circ}$
