Answer:
b = 16
Step-by-step explanation:
Use the formula of an area of a triangle:
[tex]A=\dfrac{1}{2}bc\sin A=\dfrac{1}{2}ac\sin B=\dfrac{1}{2}ab\sin C[/tex]
Therefore we have the equation:
[tex]\dfrac{1}{2}bc\sin A=\dfrac{1}{2}ac\sin B[/tex] multiply both sides by 2
[tex]bc\sin A=ac\sin B[/tex] divide both sides by c
[tex]b\sin A=a\sin B[/tex] divide both sides by sin A
[tex]b=\dfrac{a\sin B}{\sin A}[/tex]
We have
[tex]\sin A=0.3,\ \sin B=0.4,\ a=12[/tex]
Substitute:
[tex]b=\dfrac{(12)(0.4)}{0.3}=\dfrac{4.8}{0.3}=\dfrac{48}{3}=16[/tex]
