To determine the value of [tex]\(\cos 30^{\circ}\)[/tex], let's consider the options provided and identify the one that correctly represents the value.
First, let's recall the exact value:
[tex]\[
\cos 30^{\circ} = \frac{\sqrt{3}}{2}
\][/tex]
The options given are:
A. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
B. 1
C. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
D. [tex]\(\frac{1}{2}\)[/tex]
E. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
F. [tex]\(\sqrt{3}\)[/tex]
We match the value [tex]\(\cos 30^{\circ} = 0.8660254037844387\)[/tex] with the options provided. Noting that the decimal representation of [tex]\(\cos 30^{\circ}\)[/tex]:
[tex]\[
0.8660254037844387
\][/tex]
is equivalent to the exact value:
[tex]\[
\frac{\sqrt{3}}{2}
\][/tex]
Thus, the correct answer among the options is:
[tex]\[
\boxed{A. \frac{\sqrt{3}}{2}}
\][/tex]
