If arcs of same length in two circles subtend angles of `30^0a n d45^0` at their centers, find the ratios of their radii.

Explanation

Let `r_(1)" and "r_2` be the radii of the given circles and let their arcs be same length s subtending angles of `60^(@)" and " 75^(@)` at their centers. Now,
`60^@=(60xxpi/180)^R=(pi/3)^R`
and `75^(@)=(15xxpi/180)^R=((5pi)/12)^R`
`:. Pi/3=s/r_1" and " (5pi)/12=s/sr_2`
`rArr pi/3r_1=S " and " (5pi)/12r_(2)=s`
`rArr pi/3r_1=(5pi)/12r_2 rArr4r_1=5r_2 rArr r_(1)/r_2=5/4`
Hence, `r_1:r_2=5:4`.