Q. 194.3( 3 Votes )

# Two ships leave a port at the same time. One goes 24 km/hr in the direction N 38^{o} E and other travels 32 km/hr in the direction S 52^{o} 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

∴ FG^{2} = EF^{2} + EG^{2}

⇒ FG =

=

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

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