Answer
$\tan 171^{\circ} 40'$ = -0.1465
Work Step by Step
Given function-
$\tan 171^{\circ} 40'$
We have to convert it to decimal degrees first-
$\tan 171^{\circ} 40'$ = $\tan (171^{\circ} + 40')$
= $\tan (171^{\circ} + (\frac{40}{60})^{\circ})$
= $\tan (171^{\circ} + (0.6667)^{\circ})$
= $\tan 171.6667^{\circ} $
Using calculator in degree mode-
171.6667 → $\tan$
$\tan 171.6667^{\circ}$ = -0.1464778373
Rounding it to four places past the decimal point-
$\tan 171.6667^{\circ}$ = -0.1465
or
$\tan 171^{\circ} 40'$ = -0.1465
