Question

The length of an arc of a circle of radius 5 cm subtending a central angle measuring ${15}^{\circ }=\frac{a\pi }{12}$. Find $a$.

Answer 1

Let s be the length of the arc subtending an angle ${\theta }^R$ at the centre of a circle of radius r. Then, $\theta =s/r$.
Here, $r=5$ cm and $\theta ={15}^{\circ }={(15\times \frac{\pi }{180})}^R={\left(\frac{\pi }{12}\right)}^R$
$\therefore$ $\theta =\frac{s}{r}$ or $\frac{\pi }{12}=\frac{s}{5}$ or $s=\frac{5\pi }{12}$ cm
Ans: 5