Thread: Law of Cosines

Could someone please help me with this problem. Thanks

Two ships leave harbor at the same time. The first sails N 15 degrees W at 25 knots (a knot is one nautical mile per hour). The second sails N 32 degrees E at 20 knots. After 2 hr, how far apart are the ships?

From N15W to N32E, the whole angle is 15+32 = 47 degrees.
After 2 hours, 25*2 = 50 nautical miles, 20*2 = 40 nautical miles.
So the figure is a triangle with known two sides and their included angle.
If x = the unknown side, which is the distance between the ships after 2 hours,then, by Law of Cosines,
x^2 = (50)^2 +(40)^2 -2(50)(40)cos(47deg)

Continue that and you will get the answer.