Question

Find the length of STV in the figure.

Answer 1

Answer: The length of STV is about 76.83 in.

Step-by-step explanation:

The length of an arc is given by :-

$l=\frac{\theta}{360^{\circ}}\times2\pi r$, where r= radius of the cirle, $\theta$ is the central angke made by arc.

As per given , Radius of the circle : r= 20 in

Central angle of arc SCV = $140^{\circ}$

Then, Central angle of arc SCV = $360^{\circ}-140^{\circ}=220^{\circ}$

Then, the length of the arc STV =

$l=\frac{220^{\circ}}{360^{\circ}}\times2(\frac{22}{7}) (20)\\\\=\frac{11}{18}\times\frac{880}{7}\\\\=76.8253968254\approx76.83\text{ in.}$

Hence, the length of STV is about 76.83 in.