To determine which option correctly represents [tex]\(\sin 16^\circ\)[/tex], we'll compare the known value of [tex]\(\sin 16^\circ\)[/tex] with the provided choices.
First, the known value of [tex]\(\sin 16^\circ\)[/tex] is approximately [tex]\(0.2756\)[/tex].
Now, let's compare this with each option by evaluating the fractions:
1. Option A: [tex]\(\frac{7}{24}\)[/tex]
[tex]\[
\frac{7}{24} = 0.2917 \quad \text{(approximately)}
\][/tex]
This is close but slightly higher than [tex]\(0.2756\)[/tex].
2. Option B: [tex]\(\frac{24}{7}\)[/tex]
[tex]\[
\frac{24}{7} = 3.4286 \quad \text{(approximately)}
\][/tex]
This value is much larger than [tex]\(0.2756\)[/tex].
3. Option C: [tex]\(\frac{7}{25}\)[/tex]
[tex]\[
\frac{7}{25} = 0.28
\][/tex]
This is very close to [tex]\(0.2756\)[/tex], with only a slight deviation.
4. Option D: [tex]\(\frac{24}{25}\)[/tex]
[tex]\[
\frac{24}{25} = 0.96
\][/tex]
This value is significantly larger than [tex]\(0.2756\)[/tex].
From these comparisons, it is evident that the closest match to [tex]\(\sin 16^\circ \approx 0.2756\)[/tex] is option C:
[tex]\[
\frac{7}{25} = 0.28
\][/tex]
Therefore, the answer is:
C. [tex]\(\frac{7}{25}\)[/tex]
