Answer
$\theta$ = $55.5^{\circ}$
Work Step by Step
Given, $\cot\theta$ = $0.6873$
We will calculate $\tan\theta$ first as calculator does not have $\cot^{-1}$ key.
Using reciprocal identity-
$\tan\theta$ = $\frac{1}{\cot\theta}$ = $\frac{1}{0.6873}$
Using calculator-(0.6873 → $\frac{1}{x}$)
$\tan\theta$ = $1.4549687182$
Therefore-
$\theta$ = $\tan^{-1} 1.4549687182$
Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI
Using calculator in degree mode-(1.4549687182→ $\tan^{-1}$)
$\theta$ = $(55.499259022) ^{\circ}$
On rounding to the nearest tenth of a degree-
$\theta$ = $55.5^{\circ}$
