Question:
Two boats leave a port at the same time. One travels 60 km in the direction N 500 E while the other travels 50 km in the direction S 700 E. What is the distance between the boats?
Solution:
Both the boats starts from $A$ and boat 1 reaches at $B$ and boat 2 reaches at $C$.
Here, $A B=60 \mathrm{Km}$ and $A C=50 \mathrm{Km}$
So, the net distance between ta boats is:
$|\overrightarrow{\mathrm{BC}}|=|\overrightarrow{\mathrm{AC}}-\overrightarrow{\mathrm{AB}}|$
$=\sqrt{60^{2}+50^{2}-2.60 .50 \cdot \cos 60^{0}}$
$=\sqrt{3600+2500-3000}$
$=55.67 \mathrm{Km}$