SOLUTION: Two trains leave a station on different tracks. The tracks make an angle of 120 degree with the as vertex. The first train travels at an average speed of 100km/hr. and the second t

Algebra ->  Trigonometry-basics -> SOLUTION: Two trains leave a station on different tracks. The tracks make an angle of 120 degree with the as vertex. The first train travels at an average speed of 100km/hr. and the second t      Log On


   

Question 678685: Two trains leave a station on different tracks. The tracks make an angle of 120 degree with the as vertex. The first train travels at an average speed of 100km/hr. and the second train travels at an average of 65km/hr. How far apart are the trains after 2 hours?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The first train traveling at an average speed of 100km/hr for 2 hours, covers a distance (in km) of
2%2A100=200.
The second train traveling at an average speed of 85km/hr for 2 hours, covers a distance (in km) of
2%2A85=170.
The Law of Cosines says that in triangle ABC c%5E2=a%5E2%2Bb%5E2-2ab%2Acos%28C%29
So we can calculate the distance between the two trains after 2 hours (side c of the triangle.
c%5E2=200%5E2%2B170%5E2-2%2A200%2A170%2Acos%28120%5Eo%29
c%5E2=200%5E2%2B170%5E2-2%2A200%2A170%2A%28-0.5%29
c%5E2=40000%2B28900%2B34000
c%5E2=102900
c=sqrt%28102900%29
c=321 (approx.)
The trains are highlight%28321%29km apart after 2 hours