Answer
$\theta$ = $10^{\circ}10'$
Work Step by Step
Given, $\cot\theta$ = $5.5764$
We will calculate $\tan\theta$ first as calculator does not have $\cot^{-1}$ key.
Using reciprocal identity-
$\tan\theta$ = $\frac{1}{\cot\theta}$ = $\frac{1}{5.5764}$
Using calculator-(5.5764→ $\frac{1}{x}$)
$\tan\theta$ = $0.1793271645$
Therefore-
$\theta$ = $\tan^{-1} 0.1793271645$
Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI
Using calculator in degree mode-(0.1793271645→ $\tan^{-1}$)
$\theta$ = $(10.166628552) ^{\circ}$
$\theta$ = $10^{\circ} + (0.166628552)^{\circ}$
$\theta$ = $10^{\circ} +( 0.166628552\times60)'$
(Recall $1^{\circ}$ = $60'$)
$\theta$ = $10^{\circ} +10'$ (Rounding to the nearest minute)
$\theta$ = $10^{\circ}10'$
