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Q.
Find the length of an arc of a circle of radius $3 \,cm$, if the angle subtended at the centre is $30^{\circ}$. $(\pi = 3.14)$
Trigonometric Functions
Solution:
Let $l$ be the length of the arc. We know that,
Angle $\theta=\frac{l}{r}$, where $\theta$ is in radian.
Given, $r = 3\, cm$,
$\theta=30^{\circ}=30\times\frac{\pi}{180}=\frac{\pi}{6}$ rad
On putting the values of $r$ and $\theta$, we get
$\frac{\pi}{6}=\frac{l}{3}$
$\Rightarrow l=\frac{\pi}{2}=\frac{3.14}{2}$
$=1.57\,cm$