Question

Use Point P to find the length of the arc. Round to the nearest hundredth

Answer 1

(a)3.67 Inches

(b)17.45 feet

Step-by-step explanation:

Part 1

If FI=12 yards, then:

• Radius, r= 6 yards

The measure of the central angle at GF=35 degrees

`\begin{gathered} \text{Length of an arc=}(\theta)/(360)*2\pi r \\ \theta=\text{Central Angle} \\ r=\text{Radius} \end{gathered}`

Therefore:

`\begin{gathered} \text{Length of arc GF=}(35)/(360)*2*\pi*6 \\ =3.67\text{ inches (to the nearest hundredth)} \end{gathered}`

Part 2

If PH=8 feet, then:

• Radius, r= 8 feet

The measure of the central angle at FH=35+90=125 degrees

Therefore:

`\begin{gathered} \text{Length of arc FH=}(125)/(360)*2*\pi*8 \\ =17.45\text{ f}eet\text{ (to the nearest hundredth)} \end{gathered}`