Two ships leave a port at the same time. One goes 24 km per hour in the direction `N 45oE`and other travels 32 km per hour in the direction `S 75oE`. Find the distance between the ships at the end of 3 hours.

Explanation

With the given details, we can construct a diagram.

Please refer to video for the diagram.

From the diagram, we can see that,

`/_AOB = 60^@, OA = 72km, OB = 96km`

So, `AB = sqrt(OA^2+OB^2-2*OA*OB*cos60^@)`

`AB = sqrt(72^2+96^2-2*72*96*1/2)`

`AB = sqrt(24^2*3^2+24^2*4^2-24^2*3*4)`

`AB = 24sqrt(9+16-12) = 24sqrt13 = 86.53km`

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