Two planes take off at the same time from an airport. how far apart are they after 2 hours?

Question

Two planes take off at the same time from an airport.The first plane is flying at 272 miles per hour on a course of 155.0°. The second plane is flying in the direction 165.0° at 357 miles per hour. Assuming there are no wind currents blowing, how far apart are they after 2 hours?

Answer 1

If you draw this out you will see that you have a triangle with one side equal to 272x2=544, another side equal to 357x2=714 and the included angle between them equal to 165°-155°=10°. We can solve for the third side, which is the distance between the planes after 2 hours of flight, by using the Law of Cosines:

a²=b²+c²-2bccosA where

a=distance needed

b=714

c=544

A=10°

Plugging these numbers into this equation and solving for "a" you will get a≅201.75 miles.

Hope this helps!