Answer: The length of STV is about 76.83 in.
Step-by-step explanation:
The length of an arc is given by :-
[tex]l=\frac{\theta}{360^{\circ}}\times2\pi r[/tex], where r= radius of the cirle, [tex]\theta[/tex] is the central angke made by arc.
As per given , Radius of the circle : r= 20 in
Central angle of arc SCV = [tex]140^{\circ}[/tex]
Then, Central angle of arc SCV = [tex]360^{\circ}-140^{\circ}=220^{\circ}[/tex]
Then, the length of the arc STV =
[tex]l=\frac{220^{\circ}}{360^{\circ}}\times2(\frac{22}{7}) (20)\\\\=\frac{11}{18}\times\frac{880}{7}\\\\=76.8253968254\approx76.83\text{ in.}[/tex]
Hence, the length of STV is about 76.83 in.
