Answer: Choice C) [tex]\frac{\sin(23)}{6.2} = \frac{\sin(85)}{b}[/tex]
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Explanation:
The angle opposite side b is 85 degrees. So we'll involve either the fraction [tex]\frac{\sin(85)}{b}[/tex] or [tex]\frac{b}{\sin(85)}[/tex]. In this case, we will use the first fraction. This is due to all of the answer choices having sine on top.
The other fraction must have sine on top as well.
The known side is AB = 6.2; the opposite angle is C = 23 which you find by solving A+B+C = 180 and plugging in A = 72 and B = 85.
So the other fraction we'll use is [tex]\frac{\sin(23)}{6.2}[/tex]
Overall, the proportion we can set up is
[tex]\frac{\sin(23)}{6.2} = \frac{\sin(85)}{b}[/tex]
which points to choice C as the final answer.
