To determine the value of [tex]\(\sin 16^{\circ}\)[/tex], we start by referring to the known answer:
The value of [tex]\(\sin 16^{\circ}\)[/tex] is approximately 0.2756.
Let's compare this value with each given option:
A. [tex]\(\frac{7}{24}\)[/tex]:
[tex]\[ \frac{7}{24} \approx 0.2917 \][/tex]
B. [tex]\(\frac{24}{7}\)[/tex]:
[tex]\[ \frac{24}{7} \approx 3.4286 \][/tex]
C. [tex]\(\frac{7}{25}\)[/tex]:
[tex]\[ \frac{7}{25} = 0.28 \][/tex]
D. [tex]\(\frac{24}{25}\)[/tex]:
[tex]\[ \frac{24}{25} = 0.96 \][/tex]
Comparing these values:
- [tex]\(\frac{7}{24}\)[/tex] (approximately 0.2917) is not approximately 0.2756.
- [tex]\(\frac{24}{7}\)[/tex] (approximately 3.4286) is significantly larger than 0.2756.
- [tex]\(\frac{7}{25}\)[/tex] (exactly 0.28) is very close to 0.2756, but not exact.
- [tex]\(\frac{24}{25}\)[/tex] (exactly 0.96) is much larger than 0.2756.
Thus, none of the given fractions exactly equal 0.2756. However, the closest numerical fraction to 0.2756 is closest to option C, since [tex]\(\frac{7}{25} = 0.28\)[/tex] is very close to 0.2756.
While none of the options are perfect, if we had to choose the best match,
the answer would be closest to:
[tex]\[ \boxed{\frac{7}{25}} \][/tex]
However, it is important to note that there isn't an exactly matching result among the given answer choices.
