To determine the value of [tex]\(\sin 67^{\circ}\)[/tex], we need to find its trigonometric value.
First, we know that the sine function for an angle in degrees can be found using the relation:
[tex]\[
\sin \theta
\][/tex]
For [tex]\(\theta = 67^{\circ}\)[/tex]:
[tex]\[
\sin 67^{\circ} \approx 0.9205048534524404
\][/tex]
Next, let's compare this numerical value to the given multiple-choice options:
A. [tex]\(\frac{5}{12} \approx 0.4167\)[/tex]
B. [tex]\(\frac{5}{13} \approx 0.3846\)[/tex]
C. [tex]\(\frac{12}{5} = 2.4\)[/tex] (Note: Since [tex]\(\sin \theta\)[/tex] values range from -1 to 1, this option is not viable.)
D. [tex]\(\frac{12}{13} \approx 0.9231\)[/tex]
Given that [tex]\(0.9205048534524404\)[/tex] is closest to [tex]\(0.9231\)[/tex], the best-matching multiple-choice option is:
D. [tex]\(\frac{12}{13}\)[/tex].
So, the correct answer is:
D. [tex]\(\frac{12}{13}\)[/tex].
