From the problem we have
In △ABC, m∠A=52°, c=11, and m∠B=19°.
Draw the diagram with the help of given information, (see the attached image)
Now using Sine Law in the Triangle ABC, we can write
Now from Triangle ABC , we can write
[tex] <C=180-<A-<B\\
\\
<C=180-52-19\\
\\
<C=109\\ [/tex]
[tex] \frac{a}{sin52}=\frac{11}{sin109} \\ [/tex]
Now simplify , we get
[tex] \Rightarrow a=\frac{11}{sin109}*sin52\\
\\
\Rightarrow a=\frac{11}{0.9455}*0.7880\\
\\
\Rightarrow a=9.1676 \approx 9.2\\
[/tex]
