Question

If TR = 9 ft, find the length of PS. Round to the nearest tenth place. g Р T R. 16 S Use 3.14 for π

Answer 1

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,

`(\theta)/(360)*2\pi r`

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:

`\begin{gathered} (164)/(360)*2\pi(9) \\ =(164)/(360)*18\pi \\ =(82)/(180)*18\pi \\ =25.76 \end{gathered}`

Rounding the answer to the nearest tenth,

Answer

25.8 ft