To determine the value of [tex]\( a \)[/tex], we start by using the given fact that [tex]\(\sin 30^{\circ} = \frac{1}{2}\)[/tex].
We're tasked with finding [tex]\( a \)[/tex], where:
[tex]\[ a = \sin 30^{\circ} \][/tex]
Given that:
[tex]\[ \sin 30^{\circ} = \frac{1}{2} \][/tex]
We can substitute this value directly into the expression for [tex]\( a \)[/tex]:
[tex]\[ a = \sin 30^{\circ} = \frac{1}{2} \][/tex]
To express [tex]\( \frac{1}{2} \)[/tex] in a decimal form, we get:
[tex]\[ \frac{1}{2} = 0.5 \][/tex]
Therefore, the value of [tex]\( a \)[/tex] is:
[tex]\[ a = 0.5 \][/tex]
Looking at the provided options:
A. 18
B. 15.59
C. 9
D. 4.5
None of these options are equivalent to 0.5.
Thus, it appears that there's a mismatch between the given options and the calculated value. If 0.5 is truly the correct value for [tex]\( a \)[/tex], none of the provided options are correct. However, based on our calculations, the final value of [tex]\( a \)[/tex] is indeed:
[tex]\[ a = 0.5 \][/tex]
