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Two boats leave a port at the same time....

Two boats leave a port at the same time. One travels 60 km in the direction `N 50^(@)E` while the other travale 50 km in the direction `S70^(@)E`. What is the distance between the boats ?

Text Solution

Verified by Experts

The correct Answer is:
`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.
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