Answer:
Rounded to the nearest tenth: c = 32.2
Step-by-step explanation:
We can use the Law of Sines to solve the problem.
Recall this useful Law for triangles:
[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]
so we can use it for the data and unknown of our case ([tex]A=72^o[/tex], [tex]C=50^o[/tex], [tex]a=40[/tex], and c what we need to find:
[tex]\frac{a}{sin(A)} =\frac{c}{sin(C)}\\\frac{40}{sin(72^o)} =\frac{c}{sin(50^o)}\\c=\frac{40\,*\,sin(50^o)}{sin(72^o)}\\c=32.21867[/tex]
and this rounded to the nearest tenth is: c = 32.2
