Answer:
[tex]AC=8\sqrt{2}\text{ in}[/tex]
Explanations:
Given the sketch of the triangle shown below:
From the figure shown, the measure of the interior quadrilateral is 360 degrees
30 + 30 + 30 + reflex = 360
reflex angle = 360 - 90
reflex angle = 270 degrees
Since AB = BC = 8in
To determine the measure of AC, we will use the sine rule
[tex]\begin{gathered} \frac{AC}{sin\angle ABC}=\frac{BC}{sin\angle BAC} \\ \frac{AC}{sin90}=\frac{8}{sin45} \\ \end{gathered}[/tex]
Simplify the result
[tex]\begin{gathered} ACsin45=8sin90 \\ AC=\frac{8sin90}{sin45} \\ AC=\frac{8(1)}{\frac{1}{\sqrt{2}}} \\ AC=8\sqrt{2}\text{ in} \end{gathered}[/tex]
