Find the length of STV in the figure.

Question

asked Aug 17, 2021 134k views

2 Answers

Magnus Johansson · Answer 1 · 2021-08-23T07:39:44+0000

Answer: The length of STV is about 76.83 in.

Explanation:

The length of an arc is given by :-

$l=(\theta)/(360^(\circ))*2\pi r$ , 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 =

$l=(220^(\circ))/(360^(\circ))*2((22)/(7)) (20)\\\\=(11)/(18)*(880)/(7)\\\\=76.8253968254\approx76.83\text{ in.}$

Hence, the length of STV is about 76.83 in.