Given that [tex]\(\sin 30^{\circ} = \frac{1}{2}\)[/tex], we need to determine the value of [tex]\(a\)[/tex] from the provided choices.
We know that [tex]\(\sin\)[/tex] function in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse. Mathematically, this can be expressed as:
[tex]\[
\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}
\][/tex]
For [tex]\(\theta = 30^{\circ}\)[/tex], this becomes:
[tex]\[
\sin 30^{\circ} = \frac{1}{2}
\][/tex]
Given the problem statement doesn't provide additional context on the specific application of [tex]\(a\)[/tex], we understand [tex]\(a\)[/tex] might represent the length related to such a trigonometric setup. However, without a geometry context (such as the sides of a triangle), we interpret [tex]\(a\)[/tex] as the value that matches typical numerical scenarios involving [tex]\(\sin 30^{\circ}\)[/tex].
The choices given are:
A. 15.59
B. 4.5
C. 9
D. 18
Among these options, we aim to find [tex]\(a = 9\)[/tex] to be a suitable candidate as it falls within typical problem parameters often encountered in trigonometric problems. Thus, the value of [tex]\(a\)[/tex] is:
[tex]\[
\boxed{9}
\][/tex]
