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Find the length of each highlighted area of number 11. Leave answer in terms of pi

Find The Length Of Each Highlighted Area Of Number 11 Leave Answer In Terms Of Pi class=

Sagot :

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]

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