length of arc PS is 17.17 ft
Explanation:
PR is a diameter.
The angle between PR is 180 degrees (sum of angles on a line)
Hence, arc PR = 180°
To get the length of arc PS, we will apply the formula for length of an arc:
[tex]\begin{gathered} In\text{ degr}ees, \\ \text{length of an arc = }\frac{\theta}{360}\times2\pi r \end{gathered}[/tex]
TR = 6 ft
TR = radius
r = 6 ft
θ = angle between the arc we are looking for its length
θ = arc PS
arc PS + arc RS = arc PR
arc RS = 16°
arc PS + 16° = 180°
arc PS = 180 - 16
arc PS = 164°
θ = 164°
Substitute the values into the formula:
[tex]\begin{gathered} \text{length of the arc }=\frac{164}{360}\times2\times\pi\times6 \\ \text{length of the arc }=\text{ }17.17 \end{gathered}[/tex]
