Answer
$\cos 24^{\circ} 30'$ = 0.9100
Work Step by Step
First we will convert $24^{\circ}30′$ to decimal degrees, let's break it as-
$24^{\circ}30′$ = $24^{\circ}$ + $30′$
Now on dividing 30′ by 60, we have the number of "decimal degrees" equivalent to 30′ (as $1^{\circ}$=60′)
Therefore
$24^{\circ}30′$ = $24^{\circ} + (\frac{30}{60})^{\circ}$
$24^{\circ}30′$ = $24^{\circ} + 0.5^{\circ}$
$24^{\circ}30′$= $24.5^{\circ}$
Now
Using calculator in degree mode-
$\cos 24.5^{\circ}$ = 0.9099612709
Rounding it to four places past the decimal point-
$\cos 24.5^{\circ}$ = 0.9100
Therefore-
$\cos 24^{\circ} 30'$ = 0.9100
