Respuesta :
Answer:
Angle C is 128.49°
Step-by-step explanation:
Recall the Law of Sines
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
Set up a proportion with the given information to find angle B
[tex]\frac{sin30^\circ}{15}=\frac{sinB}{11}[/tex]
[tex]11sin30^\circ=15sinB[/tex]
[tex]11(0.5)=15sinB[/tex]
[tex]5.5=15sinB[/tex]
[tex]\frac{5.5}{15}=sinB[/tex]
[tex]B=sin^{-1}(\frac{5.5}{15})[/tex]
[tex]B\approx21.51^\circ[/tex]
Use angles A and B to find angle C by the Triangle Angle Sum Theorem
[tex]180^\circ=A^\circ+B^\circ+C^\circ[/tex]
[tex]180^\circ=30^\circ+21.51^\circ+C^\circ[/tex]
[tex]180^\circ=51.51^\circ+C^\circ[/tex]
[tex]128.49^\circ=C^\circ[/tex]
Therefore, angle C is 128.49°
