Answer:
C = 64.145º
Step-by-step explanation:
The Law of Sines is as follows:
[tex]\frac{sinA}{a}[/tex] = [tex]\frac{sinB}{b}[/tex] = [tex]\frac{sinC}{c}[/tex]
The problem can be draw as the picture attached.
Now, the values of the sides and angles can be substituted into the Law of Sines, and because all parts are equal, only two are needed:
[tex]\frac{sin40}{5}[/tex] = [tex]\frac{sinC}{7}[/tex]
Next, cross-multiply:
7sin40º = 5sinC
Then, divide both sides by 5:
[tex]\frac{7sin40}{5}[/tex] = sinC
Finally, take the inverse sin of the left side and convert into a decimal:
C = [tex]sin^{-1}[/tex]([tex]\frac{7sin40}{5}[/tex])
C = 64.145
