To find the value of \(\sin 16^{\circ}\), we need to compare the given options with the actual sine value of 16 degrees.
### Step-by-Step Solution:
1. Convert Degrees to Radians:
The sine function in most contexts uses radians, so we first need to convert 16 degrees to radians.
[tex]\[
\text{Radians} = 16^\circ \times \frac{\pi}{180^\circ}
\][/tex]
However, the key point here is to use the correct value corresponding to sine of 16 degrees.
2. Approximate the Value:
From trigonometric tables or a calculator, we find that:
[tex]\[
\sin 16^{\circ} \approx 0.2756
\][/tex]
3. Evaluate Each Option:
Next, we convert each fraction to a decimal to compare with 0.2756.
- Option A: \(\frac{24}{7} \approx 3.4286\)
- Option B: \(\frac{24}{25} = 0.96\)
- Option C: \(\frac{7}{25} = 0.28\)
- Option D: \(\frac{7}{24} \approx 0.2917\)
We see that amongst these values, \(\frac{7}{25}\) \(\approx 0.28\) is the closest to 0.2756.
4. Identify the Closest Match:
Since \(\frac{7}{25}\) is approximately 0.28, which is closest to the actual sine value of 16 degrees (0.2756), we conclude that the correct match is option C.
### Conclusion:
[tex]\[
\boxed{C}
\][/tex]
Thus, the value of [tex]\(\sin 16^{\circ}\)[/tex] is best approximated by [tex]\(\frac{7}{25}\)[/tex].
