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.
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