AC=14.7
Explanation
Step 1
given the right triangle
a)let
[tex]\begin{gathered} angle=30 \\ opposite\text{ side=BC=6}\sqrt{2} \\ adjacent\text{ side=x} \end{gathered}[/tex]
hence , we need a trigonometric function that relates those values, it is
[tex]tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}}[/tex]
replace and solve for x(AC)
[tex]\begin{gathered} tan\text{ 30}=\frac{6\sqrt{2}}{x} \\ x=\frac{6\sqrt{2}}{tan\text{ 30}} \\ x=\frac{6\sqrt{2}}{\frac{1}{\sqrt{3}}}=\frac{6\sqrt{2}\sqrt{3}}{1} \\ x=14.6969 \\ rounded \\ x=14.7 \end{gathered}[/tex]
therefore, the answer is 14.7 ( decimal form)
I hope this helps you
