To find the value of [tex]\(\sin 28^{\circ}\)[/tex], we start by understanding that the sine of an angle in degrees can be computed using trigonometric functions. Given the continuous nature of trigonometric functions, the exact value might not correspond to a simple fraction, but we'll scrutinize the possibilities.
The sine of an angle represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right-angled triangle.
We have the following options:
A. [tex]\(\frac{8}{15}\)[/tex]
B. [tex]\(\frac{15}{8}\)[/tex]
C. [tex]\(\frac{8}{17}\)[/tex]
D. [tex]\(\frac{15}{17}\)[/tex]
Our task is to determine the correct value that approximates [tex]\(\sin 28^{\circ}\)[/tex].
Given the result:
[tex]\[
\sin 28^{\circ} \approx 0.4694715627858908
\][/tex]
Let’s evaluate the given options as decimal approximations:
A. [tex]\(\frac{8}{15} \approx 0.5333333\)[/tex]
B. [tex]\(\frac{15}{8} \approx 1.875\)[/tex]
C. [tex]\(\frac{8}{17} \approx 0.4705882\)[/tex]
D. [tex]\(\frac{15}{17} \approx 0.8823529\)[/tex]
Comparing these approximate values with [tex]\(0.4694715627858908\)[/tex]:
- [tex]\(\frac{8}{15} \approx 0.5333333\)[/tex]
- [tex]\(\frac{15}{8} \approx 1.875\)[/tex]
- [tex]\(\frac{8}{17} \approx 0.4705882\)[/tex]
- [tex]\(\frac{15}{17} \approx 0.8823529\)[/tex]
We see that [tex]\(\frac{8}{17}\)[/tex] is the closest approximation to the value [tex]\(0.4694715627858908\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{8}{17}}
\][/tex]
