Question

if an arc has a measure of 97 degrees, and the circle has radius=10, what is the arc length

Answer 1

$\textbf{Formula used:}$

$\boxed{\text{Arc length of sector=}\frac{\theta}{360^{\circ}}{\times}2\pi\,r\;\text{units}}$

$\textbf{Given: }$

$\text{Central angle, \theta=97^{\circ} }$

$\text{Radius, r=10 cm}$

$\text{Now,}$

$\text{Arc length of the sector}$

$=\frac{\theta}{360^{\circ}}{\times}2\pi\,r$

$=\frac{97^{\circ}}{360^{\circ}}{\times}2{\times}\frac{22}{7}{\times}10$

$=\frac{97^{\circ}}{36^{\circ}}{\times}2{\times}\frac{22}{7}$

$=\frac{97^{\circ}}{18^{\circ}}{\times}\frac{22}{7}$

$=\frac{97^{\circ}}{9^{\circ}}{\times}\frac{11}{7}$

$=\frac{1067}{63}$

$=16.94\;\text{units}$

$\therefore\textbf{Arc length is 16.94 units}$