Q. 194.3( 3 Votes )

Two ships leave a port at the same time. One goes 24 km/hr in the direction N 38o E and other travels 32 km/hr in the direction S 52o E. Find the distance between the ships at the end of 3 hrs.

Answer :


The key point to solve the problem:


The idea of cosine formula –


Cos C = Cos A = Cos B =


According to the question:


One ship goes in north east direction while other in southeast direction.


After 3 hours ship going in north east will be at a distance


Speed of ship A = 24km/hr


Speed of ship B = 32km/hr


Distance travelled by ship A after 3 hours = 24 × 3 = 72 km


Distance travelled by ship B after 3 hours = 32 × 3 = 96 km


We have to find the distance between the ships :


See the figure :



Now in Δ EFG,


EF is the distance traveled by ship A


And EG is the distance traveled by ship B


we have to find FG,


Applying cosine formula, we have-


Cos E =


Cos E = Cos 90° = 0


FG2 = EF2 + EG2


FG =


=


distance between ships after 3 hours = 120 KM ….ans


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