Please try to solve this problem using fewer steps as possib

Please try to solve this problem using fewer steps as possible, with clarifying the shortcuts and the formulas used.

2. Two ships leave a harbor at the same time. Ship A travels on a bearing of N30 W at 4 miles per hour while ship B travels on a bearing of S30°W at 3 miles per hour (as pictured below). After three hours exactly how far apart are the two ships? Ship A North 30 30 Ship B

Solution

Let the harbour is at point O

<AOB=180-(30+30)=120 degree

Speed of ship A is 4 miles per hour

Therefore after 3 hours,total distance travelled by ship A=12 miles

And total distance travelled by ship B is 9 miles

OA=12 miles

and OB= 9 miles

We have to find AB

using cosine law

AB²=OA²+OB²-2OAOB cos <AOB

AB²= 12²+9²-2(12)(9)cos 120

AB²= 333

AB=18.25miles

Therefore after 3 hours the distance between them is 18.25 miles