Solution: 24.096
Analysis:
We have a triangle and know two angles and one side of the triangle. According to the angle rule, a triangle's total intern angles equals 180 degrees. We have:
mm∠B=19°
∠A+∠B+∠C=180°
55°+19°+∠C=180°
∠C=180°-55°-19°
∠C=106°
[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex][tex]\begin{gathered} \frac{a}{sin(55)}=\frac{11}{sin(106)} \\ \\ a=\frac{11\ast sin(55)}{sin(106)}=\frac{11\ast0.82}{0.96}=9.37 \end{gathered}[/tex][tex]\begin{gathered} \frac{b}{sin(19)}=\frac{11}{sin(106)} \\ \\ b=\frac{11\ast sin(19)}{sin(106)}=\frac{11\ast0.325}{0.96}=3.726 \end{gathered}[/tex]Perimeter=a+b+c
Perimeter=9.37+3.726+11
Perimeter=24.096
