Question

The length of arc of a sector is 22 cm and its radius is 10.5 cm. Find its central angle.

Answer 1

the formula is given as:

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

where, $r=$ radius of the arc

$l=$ length of the arc

$\theta =$ central angle

Given that $r=10.5cm$ and $l=22cm$.

by substituting the values in the formula we get,

$\Rightarrow \frac{\theta }{{360}^{\circ }}\times 2\times \frac{22}{7}\times 10.5=22$

$\Rightarrow \theta =22\times {360}^{\circ }\times \frac{1}{2}\times \frac{7}{22}\times \frac{1}{10.5}$

$\therefore \theta ={120}^{\circ }$