Answer
15.055723
Work Step by Step
Converting $183^{\circ}48'$ to decimal degrees, we get
$183^{\circ}48'=183^{\circ}+\frac{48}{60}^{\circ}=183^{\circ}+0.8^{\circ}=183.8^{\circ}$
$\cot 183^{\circ}48'=\cot 183.8^{\circ}$
Now, we use the reciprocal identity $\cot\theta=\frac{1}{\tan\theta}$ to simplify the expression.
$\cot 183.8^{\circ}=\frac{1}{\tan 183.8^{\circ}}\approx15.055723$
