document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208037>Question 208037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157359 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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?<BR>\n" );
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document.write( "you have a right triangle.<BR>\n" );
document.write( "the railroad track to the train is the base of the right triangle<BR>\n" );
document.write( "the car to the railroad track is the altitude of the right triangle<BR>\n" );
document.write( "the distance from the car to the train is the hypotenuse of the right triangle.<BR>\n" );
document.write( "the 90 degree angle is at the crossing<BR>\n" );
document.write( "let point A be the car<BR>\n" );
document.write( "let point B be the crossing<BR>\n" );
document.write( "let point C be the train<BR>\n" );
document.write( "your right triangle is ABC<BR>\n" );
document.write( "your right angle is at B<BR>\n" );
document.write( "side AB is 30 meters<BR>\n" );
document.write( "side AC is 50 meters<BR>\n" );
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document.write( "you can solve for the cosine of A to get angle A<BR>\n" );
document.write( "you can solve for the sine of C to get angle C<BR>\n" );
document.write( "we'll do both.<BR>\n" );
document.write( "you should get the same answer either way.<BR>\n" );
document.write( "once you know angle A or angle C you can solve for BC which is the distance of the train from the crossing.<BR>\n" );
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document.write( "cosine A = adjacent side AB divided by hypotenuse AC = 30/50 = .6<BR>\n" );
document.write( "angle A = 53.13010235 degrees because cosine A = .6<BR>\n" );
document.write( "sine C = opposite side AB divided by hypotenuse AC  = .6<BR>\n" );
document.write( "angle C = 36.86989765 because sine C = .6<BR>\n" );
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document.write( "angle A plus angle C should equal 90 degrees which they do.<BR>\n" );
document.write( "so far so good.<BR>\n" );
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document.write( "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.<BR>\n" );
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document.write( "sine of angle A = opposite side BC divided by hypotenuse AC<BR>\n" );
document.write( "angle A = 53.13010235 degrees<BR>\n" );
document.write( "BC = x<BR>\n" );
document.write( "AC = 50<BR>\n" );
document.write( "sine of 53.13010235 = x/50<BR>\n" );
document.write( "x = 50 * sine of 53.13010235 degrees = 50 * .8 = 40 meters<BR>\n" );
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document.write( "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.<BR>\n" );
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document.write( "cosine of angle C = adjacent side BC divided by hypotenuse AC<BR>\n" );
document.write( "angle C = 36.86989765 degrees<BR>\n" );
document.write( "BC = x<BR>\n" );
document.write( "AC = 50<BR>\n" );
document.write( "cosine of 36.86989765 = x/50<BR>\n" );
document.write( "x = 50 * cosine of 36.86989765 degrees = 50 * .8 = 40 meters<BR>\n" );
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document.write( "you get the same answer either way.<BR>\n" );
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document.write( "if you have trouble visualizing it, draw your self a picture as follows:<BR>\n" );
document.write( "horizontal line on the page.<BR>\n" );
document.write( "vertical line intersecting the horizontal line in the middle of the page.<BR>\n" );
document.write( "label that intersection B.<BR>\n" );
document.write( "come down on the vertical line from the intersection about 2 inches and label that point A<BR>\n" );
document.write( "go right on the horizontal line from the intersection about 2 and 2/3 inches and label that point C<BR>\n" );
document.write( "connect point A with point C<BR>\n" );
document.write( "ABC is your right triangle.<BR>\n" );
document.write( "30 meters from A to B<BR>\n" );
document.write( "50 meters from A to C<BR>\n" );
document.write( "40 mete3rs from B to C<BR>\n" );
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document.write( " </SPAN>\n" );
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