Answer: [tex]\begin{gathered} Equation\text{ = }\frac{\theta}{360}\text{\times2}\times\text{\pi}\times r \\ Equation\text{ = }\frac{320}{360}\text{\times 2}\times\text{\pi}\times5 \\ \\ length\text{ of the arc = }\frac{80π}{9} \end{gathered}[/tex]
Explanation:
Given:
11) arc BC = 40°
highlighted arc = ?
radius = 5 in
To find:
the length of the highlighted arc
First we need to find the measure of the highlighted arc
highlighted arc + BC = 360°
highlighted arc + 40° = 360°
highlighted arc = 360 - 40
highlighted arc= 320°
The formula for length of an arc when the angle is in degrees:
[tex]\begin{gathered} Length\text{ of an arc = \theta/360 \times 2\pi r} \\ where\text{ r = radius} \\ θ=\text{ angle = highlighted arc} \end{gathered}[/tex]
Substitute the values into the formula:
[tex]\begin{gathered} length\text{ of the arc = }\frac{320}{360}\text{\times 2}\times\text{\pi}\times5 \\ \\ length\text{ of the arc = }\frac{8}{9}\times10π \\ \\ length\text{ of the arc = }\frac{80π}{9} \end{gathered}[/tex]
