document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120730>Question 1120730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bridge is going to be built across a canyon from point A to point B.   The bearing from A to B is S 28o W.   Point C is 87 miles from point A.   From point C, the bearing to point A is S 84o E and to point B is S 32o E.   Find the required length of the bridge. \r<BR>\n" );
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document.write( "Round your answer to two decmial places.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #738477 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=738477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the key here appears to be to get the angles right.<BR>\n" );
document.write( "once you do that, you can use the law of sines to find the required distances.\r<BR>\n" );
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document.write( "here's my diagram.\r<BR>\n" );
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document.write( "you are given that point B is south 28 degrees west from point A.<BR>\n" );
document.write( "that would be angle BAE in the diagram.<BR>\n" );
document.write( "AE is a perpendicular line dropped from point A.\r<BR>\n" );
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document.write( "you are given that point C is 87 miles from point A.<BR>\n" );
document.write( "that would be line segment CA in the diagram.\r<BR>\n" );
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document.write( "you are given that point A is south 84 degrees east from point C.<BR>\n" );
document.write( "that would be angle ACD in the diagram.<BR>\n" );
document.write( "CD is a perpendicular line dropped from point C.\r<BR>\n" );
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document.write( "you are given that point B is south 32 degrees east from point C.<BR>\n" );
document.write( "that would be angle BCD in the diagram.<BR>\n" );
document.write( "CD is a perpendicular line dropped from point C.\r<BR>\n" );
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document.write( "line segment DE is a horizontal line drawn from point D through point B extending to point E.\r<BR>\n" );
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document.write( "angle CDB and angle AEB are both right angles because they are the intersection of horizontal and vertical lines.\r<BR>\n" );
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document.write( "that makes angle CDB and AEB both equal to 90 degrees.\r<BR>\n" );
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document.write( "angle ABE is equal to 62 degrees because it is part of triangle ABE and the sum of the angles of a triangle is equal to 180 degrees.\r<BR>\n" );
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document.write( "similarly, angle CBD is equal to 58 degrees.\r<BR>\n" );
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document.write( "angle CBA is equal to 60 degrees because it is the third angle that makes up the 180 degree angle DBE.<BR>\n" );
document.write( "angle DBE is equal to angle CBD plus CBA plus ABE.\r<BR>\n" );
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document.write( "angle ACB is equal to 52 degrees because it is equal to angle ACD minus angle BCD.<BR>\n" );
document.write( "the sum of angles BCD and ACB is equal to 32 + 52 = 84 degrees which is angle ACD.\r<BR>\n" );
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document.write( "looks like all the angles are take care of.\r<BR>\n" );
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document.write( "you have triangle ABC with side AC = 87.<BR>\n" );
document.write( "the other two sides of the triangle can be found using the law of sines.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "AB / sin(52) = 87 / sin(60).<BR>\n" );
document.write( "solve for AB to get AB = 87 * sin(52) / sin(60).\r<BR>\n" );
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document.write( "CB / sin(68) = 87 / sin(60).<BR>\n" );
document.write( "solve for CB to get CB = 87 * sin(68) / sin(60).\r<BR>\n" );
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document.write( "you will get AB = 79.16273041 and CB = 93.14391356.\r<BR>\n" );
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document.write( "you were asked to find the length of the bridge.\r<BR>\n" );
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document.write( "that would be the line segment AB = 79.16273041 miles = 79.16 miles rounded to two decimal places.\r<BR>\n" );
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document.write( "here's a reference on bearing that might be helpful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsteacher.com.au/year7/ch08_angles/07_bear/bearing.htm\" traget = \"_blank\">https://www.mathsteacher.com.au/year7/ch08_angles/07_bear/bearing.htm</a>\r<BR>\n" );
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document.write( "here's a reference on law of sines that might be helpful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www2.clarku.edu/~djoyce/trig/laws.html\" target = \"_blank\">http://www2.clarku.edu/~djoyce/trig/laws.html</a>\r<BR>\n" );
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