Question

Find the degrees the angle subtended the centre of a circle by an arc whose length $15cms$, if the radius of the circle is $25cms$.

Answer 1

Given that:-

Length of arc $\left(l\right)=15cm$

Radius of circle $\left(r\right)=25cm$

Angle subtended at the centre $\left(\theta \right)=?$

As we know that,

$l=r\theta$

$\Rightarrow \theta =\frac{l}{r}=\frac{15}{25}=\frac{3}{5}=0.6\text{radians}$

As we know that,

$1\text{radian}=\frac{180}{\pi }°$

$\therefore 0.6\text{radian}=\frac{180}{\pi }\times 0.6=\frac{180\times 7}{22}\times 0.6=34.36°=34°{36}^{\prime }$

Hence the radian and degree measure of the angle subtended at the centre of circle is $0.6$ radians and $34°{36}^{\prime }$ respectively.