Answer
$\sec 45^{\circ}54′$ = 1.4370
Work Step by Step
First we will convert $45^{\circ}54′$ to decimal degrees, let's break it as-
$45^{\circ}54′$ = $45^{\circ}$ + $54′$
Now on dividing 54′ by 60, we have the number of "decimal degrees" equivalent to 54′ (as $1^{\circ}$=60′)
Therefore
$45^{\circ}54′$ = $45^{\circ} + (\frac{54}{60})^{\circ}$
$45^{\circ}54′$ = $45^{\circ} + 0.9^{\circ}$
$45^{\circ}54′$ = $45.9^{\circ}$
Now
Using calculator in degree mode-
$\cos 45.9^{\circ}$ = 0.6959127966
$\sec 45.9^{\circ}$ = 1.4369616494
(Using $\frac{1}{x}$ key on calculator)
Rounding it to four places past the decimal point-
$\sec 45.9^{\circ}$ = 1.4370
Therefore-
$\sec 45^{\circ}54′$ = 1.4370
