Answer
$\sec 84^{\circ}48′$ = 11.0336
Work Step by Step
First we will convert $84^{\circ}48′$ to decimal degrees, let's break it as-
$84^{\circ}48′$ = $84^{\circ}$ + $48′$
Now on dividing 48′ by 60, we have the number of "decimal degrees" equivalent to 48′ (as $1^{\circ}$=60′)
Therefore
$84^{\circ}48′$ = $84^{\circ} + (\frac{48}{60})^{\circ}$
$84^{\circ}48′$ = $84^{\circ} + 0.8^{\circ}$
$84^{\circ}48′$ = $84.8^{\circ}$
Now
Using calculator in degree mode-
$\cos 84.8^{\circ}$ = 0.0906325802
$\sec 84.8^{\circ}$ = 11.033559872
(Using $\frac{1}{x}$ key on calculator)
Rounding it to four places past the decimal point-
$\sec 84.8^{\circ}$ = 11.0336
Therefore-
$\sec 84^{\circ}48′$ = 11.0336
