Question

Find the length of the highlighted arc on problem 11. Leave answer In terms of pi

Answer 1

27.925 inches

Explanation

the equation to find the arclength is

$\begin{gathered} arc\text{ length=}\frac{\theta}{360}*2\pi r \\ where \\ r\text{ is the radius } \\ a\text{ndthe angle }\theta\text{ is measured in degrees} \end{gathered}$

so

Step 1

a) let

$\begin{gathered} radius=\text{ 5 in} \\ angle=\theta=360-40=320° \end{gathered}$

b) now, replace in the equation

$\begin{gathered} arc\text{length=}\frac{\theta}{360}\text{\times2\pi r} \\ arclength=\text{ }\frac{320}{360}*2\pi *(5\text{ in\rparen} \\ arclength=\frac{320}{360}*10\pi \\ arclength=\text{ 27.925 inches} \end{gathered}$

therefore, the answer is 27.925 inches

I hope this helps you