Question

(3) Find the angle in degree subtended at
the centre of a circle by an arc whose
length is 15 cm, if the radius of the
circle is 25 cm.
​

Answer 1

Given that:-

Length of arc (l)=15cm

Radius of circle (r)=25cm

Angle subtended at the centre (θ)=?

As we know that,

l=rθ

⇒θ=  

r

l

​  

=  

25

15

​  

=  

5

3

​  

=0.6 radians

As we know that,

1 radian=  

π

180

​  

°

∴0.6 radian=  

π

180

​  

×0.6=  

22

180×7

​  

×0.6=34.36°=34°36  

′

 

Hence the radian and degree measure of the angle subtended at the centre of circle is 0.6 radians and 34°36  

′

 respectively.