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:
![\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}](/tpl/images/0702/8890/87f65.png)
so we can use it for the data and unknown of our case (
,
,
, and c what we need to find:
![\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](/tpl/images/0702/8890/e0778.png)
and this rounded to the nearest tenth is: c = 32.2