Answer:
The length of arc is [tex]L=\dfrac{9}{2}\pi[/tex] feet
D is correct
Step-by-step explanation:
Given: If the radius of a circle is 10 feet and arc subtended by an angle measuring 81°
Formula:
[tex]\theta=\dfrac{\text{Length of arc}}{\text{Radius}}[/tex]
where,
Length of arc = L?
Radius of circle, R= 10 feet
Central angle, Ф=81°
First we will change 81 degree to radian
[tex]Radian = \dfrac{\pi}{180}\times degree[/tex]
In radian [tex]=\dfrac{\pi}{180}\times 81[/tex]
Substitute the value into formula
[tex]\dfrac{\pi}{180}\times 81=\dfrac{L}{10}[/tex]
[tex]L=\dfrac{810}{180}\pi[/tex]
[tex]L=\dfrac{9}{2}\pi[/tex] feet
Hence, The length of arc is [tex]L=\dfrac{9}{2}\pi[/tex] feet
