Arc PR is half a circle, which is 180 degrees.
Arc PS + Arc SR = 180
Arc PS + 16 = 180
Arc PS = 180 - 16
Arc PS = 164°
The length of an arc is given by the formula,
[tex]\frac{\theta}{360}\times2\pi r[/tex]
Where
θ is the degree measure of the arc
r is the radius of the circle
Given
θ (Arc PS) = 164
r = TR = 9
Let's calculate length of PS:
[tex]\begin{gathered} \frac{164}{360}\times2\pi(9) \\ =\frac{164}{360}\times18\pi \\ =\frac{82}{180}\times18\pi \\ =25.76 \end{gathered}[/tex]
Rounding the answer to the nearest tenth,
Answer
25.8 ft
