Question

Hi, can you help me to solve this exercise please. If TR=6 ft, find the length “PS”

Answer 1

length of arc PS is 17.17 ft

Step-by-step 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:

`\begin{gathered} In\text{ degr}ees, \\ \text{length of an arc = }(\theta)/(360)*2\pi r \end{gathered}`

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:

`\begin{gathered} \text{length of the arc }=(164)/(360)*2*\pi*6 \\ \text{length of the arc }=\text{ }17.17 \end{gathered}`