Answer
$\theta$ = $12^{\circ}12'$
Work Step by Step
Given, $\cot\theta$ = $4.6252$
We will calculate $\tan\theta$ first as calculator does not have $\cot^{-1}$ key.
Using reciprocal identity-
$\tan\theta$ = $\frac{1}{\cot\theta}$ = $\frac{1}{4.6252}$
Using calculator-(4.6252→ $\frac{1}{x}$)
$\tan\theta$ = $0.2162068667$
Therefore-
$\theta$ = $\tan^{-1} 0.2162068667$
Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI
Using calculator in degree mode-(0.2162068667→ $\tan^{-1}$)
$\theta$ = $(12.199956965) ^{\circ}$
$\theta$ = $12^{\circ} + (0.199956965)^{\circ}$
$\theta$ = $12^{\circ} +(0.199956965\times60)'$
(Recall $1^{\circ}$ = $60'$)
$\theta$ = $12^{\circ} +12'$ (Rounding to the nearest minute)
$\theta$ = $12^{\circ}12'$
