Correct Answer - `55.68 km`
Let the original position of each boat be at O. Let A and B their respective final positions, as shown in the figure.
`"Then,"/_NOA=50^(@),50^(@)/_SOB=70^(@),OA=60" km and OB = 50 km"`
By cosine formula on `Delta AOB`, we have
`cos/_AOB=(OA^(2)+OB^(2)-AB^(2))/(2xxOAxxOB)`
`rArr" "cos60^(@)=((60)^(2)+(50)^(2)-x^(2))/(2xx60xx50)`
`rArr" "3600+2500-x^(2)=1/2xx2xx60xx50rArrx^(2)=3100rArrx=sqrt(3100)=55.68km.`
Hence, the required distance between the boast is 55.68 km.