SOLUTION: A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car’s new collision detector warns the driver that there

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car’s new collision detector warns the driver that there      Log On


   

Question 203647: A car is traveling on a road that
is perpendicular to a railroad track. When the car is
30 meters from the crossing, the car’s new collision
detector warns the driver that there is a train 50 meters
from the car and heading toward the same crossing. How
far is the train from the crossing?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw a diagram of this situation in which the railway tracks (from the train to the crossing) are represented by one leg of a right triangle and the road on which the car is traveling represents the other leg of the triangle, then the distance from the train to the car is the hypotenuse.
So we have one leg of the triangle = 30 meters and the hypotenuse = to 50 meters.
You need to find the distance. d, of the train to the crossing. Use the Pythagorean theorem: c%5E2+=+a%5E2%2Bb%5E2 where, in this problem, c = 50 meters, a = 30 meters, and d (this is the b in the formula) is unknown.
50%5E2+=+30%5E2%2Bd%5E2
2500+=+900%2Bd%5E2 Subtract 900 from both sides of the equation.
1600+=+d%5E2 Take the square root of both sides.
d+=+40meters.
The train is 40 meters from the crossing.
P.S. I hope the motorist makes it alright!