SOLUTION: Two trains leave Union station at the same time. The first train is travelling on a track with a bearing 116 degrees at 95km/h. The second train is travelling on a track with a bea

Question 1044392: Two trains leave Union station at the same time. The first train is travelling on a track with a bearing 116 degrees at 95km/h. The second train is travelling on a track with a bearing 271 degrees at 80km/h. Determine the distance between the trains 3 hours after they leave the station.
Much thanks :)
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Draw this
|===============C
|A===============================B
The AB distance is c
We have angle C, which is 155 degrees (271-116)
we have sides a and b
c^2=a^2+b^2-2ab Cos C
c^2=285^2+240^2-2(285)(240)cos C; I apologize for the error there. The a and b should be the same in both parts of the equation.
c^2=81225+57600-136800 (cos 155)=262807.91. I made the change to the answer but not to the numbers in between. You do have to add this because -136800*cos (155) is positive, because cos 155 is negative. They are going in almost opposite directions, so they do have to be in the range of 500 km apart.
c=(rounded here)512.65km
Check
Does it make sense mostly? They are going in relatively opposite bearings at 175 km/h for 3 hours. That would be 525 km. This is a reasonable answer
Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!
Two trains leave Union station at the same time. The first train is travelling on a track with a bearing 116 degrees at 95km/h. The second train is travelling on a track with a bearing 271 degrees at 80km/h. Determine the distance between the trains 3 hours after they leave the station.
Much thanks :)

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