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 collision detector warns that there is a train 50 met

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Question 208037: 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 collision detector warns that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?
Found 2 solutions by rapaljer, Theo:
Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website!
This is a right triangle, so let x = distance of train down the track.

or

Reject the negative value.

x= 40 meters

R^2

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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 collision detector warns that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?
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you have a right triangle.
the railroad track to the train is the base of the right triangle
the car to the railroad track is the altitude of the right triangle
the distance from the car to the train is the hypotenuse of the right triangle.
the 90 degree angle is at the crossing
let point A be the car
let point B be the crossing
let point C be the train
your right triangle is ABC
your right angle is at B
side AB is 30 meters
side AC is 50 meters
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you can solve for the cosine of A to get angle A
you can solve for the sine of C to get angle C
we'll do both.
you should get the same answer either way.
once you know angle A or angle C you can solve for BC which is the distance of the train from the crossing.
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cosine A = adjacent side AB divided by hypotenuse AC = 30/50 = .6
angle A = 53.13010235 degrees because cosine A = .6
sine C = opposite side AB divided by hypotenuse AC = .6
angle C = 36.86989765 because sine C = .6
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angle A plus angle C should equal 90 degrees which they do.
so far so good.
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now that you know angle A or angle C you should be able to solve for the length of BC which is the distance from the train to the crossing.
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sine of angle A = opposite side BC divided by hypotenuse AC
angle A = 53.13010235 degrees
BC = x
AC = 50
sine of 53.13010235 = x/50
x = 50 * sine of 53.13010235 degrees = 50 * .8 = 40 meters
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we have the answer and don't need to go further, but we'll go one step further to show you that angle C would have found the answer also.
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cosine of angle C = adjacent side BC divided by hypotenuse AC
angle C = 36.86989765 degrees
BC = x
AC = 50
cosine of 36.86989765 = x/50
x = 50 * cosine of 36.86989765 degrees = 50 * .8 = 40 meters
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you get the same answer either way.
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if you have trouble visualizing it, draw your self a picture as follows:
horizontal line on the page.
vertical line intersecting the horizontal line in the middle of the page.
label that intersection B.
come down on the vertical line from the intersection about 2 inches and label that point A
go right on the horizontal line from the intersection about 2 and 2/3 inches and label that point C
connect point A with point C
ABC is your right triangle.
30 meters from A to B
50 meters from A to C
40 mete3rs from B to C
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