If the arcs of the same length in two circles subtend angles of `60^(@)` and `75^(@)` at their respective centres, find the ratio of their radii?

Explanation

Let `r_(1)` and `r_(2)` be the radii of the two circles. Then,
`theta_(1) = 60^(@) = (60 xx pi/180)^(c ) = (pi/3)^(c )`
and `theta_(2) = 75^(@) = (75 xx pi/180)^(c )= ((5pi)/(12))^(c )`.
Let the length of each arcbe `l cm`. Then,
`l = r_(1)theta_(1) = r_(2)theta_(2)`.
`rArr (r_(1) xx pi/3) = (r_(2) = (5pi)/(12))`
`rArr = (r_(1))/(r_(2)) = 5/4`.
Hence, `r_(1):r_(2)= 5 : 4`.
.