Answer
1.841771
Work Step by Step
Converting $421^{\circ}30'$ to decimal degrees, we get
$421^{\circ}30'=421^{\circ}+\frac{30}{60}^{\circ}=421^{\circ}+0.5^{\circ}=421.5^{\circ}$
$\tan 421^{\circ}30'=\tan 421.5^{\circ}$
$\approx1.841771$