If the arcs of same length in two circles subtend angles of `30^(@)` and `45^(@)` at their centers, then find the ratio of their radii.

Explanation

Let `r_(1)` and `r_(2)` be the radii of the given circles and let their arcs of same length s subtend angles of `30^(@)` and `45^(@)` at their centres.
Now, `30^(@) = (30 xx pi/180)^( c)= (pi/6)^( c)` and `45^(@)= (45 xx pi/180)^( c)=(pi/4)^( c)`
`therefore pi/6 = s/r_(1)` and `pi/4 =s/r_(2)` `[therefore theta=(l/r)^( c)]`
`rArr pi/6 r_(1)=s` and `pi/4 r_(2) = s rArr pi/6 r_(1), =pi/4 r_(2) rArr 4r_(1)=6r_(2) rArr r_(1) : r_(2)=3:2`
Hence, ratio of their radii is `3:2`.