If the area of same length in two circles subtend angles of `60^(@)` and `75^(@)` at their centres. 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 `60^(@)` and `75^(@)` at their centres. ltbr gt Now, `60^(@)=(60xx(pi)/(180))^(c)=((pi)/(3))^(c)` and `75^(@)=(75xx(pi)/(180))^(c)=((5pi)/(12))^(c)`
`therefore (pi)/(3)=(s)/(r_(1))` and `(5pi)/(12)=(s)/(r_(2))`
`rArr (pi)/(3)r_(1)=s` and `(5pi)/(12)r_(2)=srArr(pi)/(3)r_(1)=(5pi)/(12)r_(2)rArr4r_(1)=5r_(3)rArrr_(1):r_(2)=5:4`.