Answer
$\tan19^{\circ}45′$ = 0.3590
Work Step by Step
First we will convert $19^{\circ}45′$ to decimal degrees, let's break it as-
$19^{\circ}45′$ = $19^{\circ}$ + $45′$
Now on dividing 45′ by 60, we have the number of "decimal degrees" equivalent to 45′ (as $1^{\circ}$=60′)
Therefore
$19^{\circ}45′$ = $19^{\circ} + (\frac{45}{60})^{\circ}$
$19^{\circ}45′$ = $19^{\circ} + 0.75^{\circ}$
$19^{\circ}45′$ = $19.75^{\circ}$
Now
Using calculator in degree mode-
$\tan 19.75^{\circ}$ = 0.3590366866
Rounding it to four places past the decimal point-
$\tan 19.75^{\circ}$ = 0.3590
Therefore-
$\tan19^{\circ}45′$ = 0.3590
