Given:
The length of arc TS = 40 in
To find:
The length of arc RS.
Solution:
Length of TS = 40 in
θ = 80°
Using arc length formula:
[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]
[tex]$40=2 \times 3.14 \times {r}\left(\frac{80}{360}\right)[/tex]
[tex]$40=6.28 \times {r}\left(\frac{2}{9}\right)[/tex]
[tex]$40=1.39\times r[/tex]
Divide by 1.39 on both sides, we get
[tex]28.7=r[/tex]
Radius = 28.7
Complete angle of circle = 360°
Angle measure of RS = 360° - 60° - 120° - 80°
Angle measure of RS = 100°
Arc length of RS:
[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]
Substitute θ = 100° and r = 28.7
[tex]$=2 \times 3.14 \times 28.7 \left(\frac{100}{360}\right)[/tex]
= 50 inch
The length of arc Rs is 50 inches.
