Answer:
[tex]AC=\frac{11\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Given that triangle ABC is a right angle triangle. Where angle C is a right angle. Also we have been given that BC = 11, B = 30°. Now we need to find the value of AC.
Apply formula:
[tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]
[tex]\tan\left(B\right)=\frac{AC}{BC}[/tex]
[tex]\tan\left(30^o\right)=\frac{AC}{11}[/tex]
[tex]\frac{1}{\sqrt{3}}=\frac{AC}{11}[/tex]
[tex]\frac{11}{\sqrt{3}}=AC[/tex]
[tex]AC=\frac{11}{\sqrt{3}}[/tex]
or
[tex]AC=\frac{11}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}[/tex]
or
[tex]AC=\frac{11\sqrt{3}}{3}[/tex]
Hence final answer is [tex]AC=\frac{11\sqrt{3}}{3}[/tex].