Correct Answer - A
In `DeltaABD`, applying since rule, we get
`(AD)/(sin pi//3)=(x)/(sin alpha)`
`rArr AD=(3)/(sqrt(2))x sin beta " "....(i)`
and in `DeltaACD`, applying since rule, we get
`(AD)/(sin//pi)=(3x)/(sin beta)`
`rArrAD=(3)/(sqrt(2))x sin beta" "....(ii)` From Eqs. (i) and (ii) , `(sqrt(3)x)/(2 sin alpha)=(3x)/(sqrt(2)sin beta)`
`rArr=(sin alpha)/(sin beta)=(1)/(sqrt(6))`