document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200155>Question 1200155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The bearing from A to C is S 52°E. the bearing from A to B is N 84°E. the bearing from B to C is S 38° W. A plane flying at 250 mph takes 2.4 hours to go from A to B. Find the distance from A to C </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834200 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "A compass bearing of something like S 52°E means we start facing directly south, then we turn 52 degrees toward the east.\r<BR>\n" );
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document.write( "Refer to this page for a few examples<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/comp.html\">http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/comp.html</a>\r<BR>\n" );
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document.write( "This is one way to draw out the diagram.<BR>\n" );
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document.write( "The diagram is to scale. It was made with GeoGebra.\r<BR>\n" );
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document.write( "The distance AB = 600 is due to the scratch work calculation shown below<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "distance = (250 mph)*(2.4 hrs)<BR>\n" );
document.write( "distance = 600 miles\r<BR>\n" );
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document.write( "Angles EAC, DAB, and GBC are the compass bearings given to us. They are marked in blue shown above.<BR>\n" );
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document.write( "<tr><TD >Angle</TD><TD >Compass Bearing</TD></tr>\r\n" );
document.write( "<tr><TD >EAC = 52</TD><TD >S 52°E</TD></tr>\r\n" );
document.write( "<tr><TD >DAB = 84</TD><TD >N 84°E</TD></tr>\r\n" );
document.write( "<tr><TD >GBC = 38</TD><TD >S 38°W</TD></tr>\r\n" );
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document.write( "</TABLE>The last two letters of each angle name tells us where we are located and where we are looking at in that exact order.<BR>\n" );
document.write( "Example: Angle EAC has \"A\" and \"C\" as the last two letters. We're located at A and look toward C.\r<BR>\n" );
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document.write( "Vertical line DE is parallel to vertical line FG.<BR>\n" );
document.write( "Segment AB is a transversal cut to these parallel lines.<BR>\n" );
document.write( "Same side interior angles DAB and FBA are supplementary (because of the parallel lines).<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "(angle DAB)+(angle FBA) = 180<BR>\n" );
document.write( "(84)+(angle FBA) = 180<BR>\n" );
document.write( "angle FBA = 180-84<BR>\n" );
document.write( "angle FBA = 96\r<BR>\n" );
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document.write( "Angle BAC is found by noticing angles EAC, BAC, and DAB are supplementary\r<BR>\n" );
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document.write( "In other words,<BR>\n" );
document.write( "(angle EAC)+(angle BAC)+(angle DAB) = 180<BR>\n" );
document.write( "and similarly<BR>\n" );
document.write( "(angle GBC)+(angle CBA)+(angle FBA) = 180<BR>\n" );
document.write( "these two equations help determine angles BAC and CBA (44 and 46 respectively)\r<BR>\n" );
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document.write( "Then we use the idea that the inner angles of a triangle add to 180<BR>\n" );
document.write( "A+B+C = 180<BR>\n" );
document.write( "44+46+C = 180<BR>\n" );
document.write( "90+C = 180<BR>\n" );
document.write( "C = 90<BR>\n" );
document.write( "Triangle ABC is a right triangle.\r<BR>\n" );
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document.write( "Since ABC is a right triangle, we have two options using the trig ratios sine and cosine<BR>\n" );
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document.write( "<tr><TD >Option 1</TD><TD >Option 2</TD></tr>\r\n" );
document.write( "<tr><TD >sin(angle) = opposite/hypotenuse<br>sin(angle ABC) = AC/AB<br>sin(46) = x/600<br>x = 600*sin(46)<br>x = 431.60388020319<br>x = 431.6</TD><TD >cos(angle) = adjacent/hypotenuse<br>cos(angle BAC) = AC/AB<br>cos(44) = x/600<br>x = 600*cos(44)<br>x = 431.60388020319<br>x = 431.6</TD></tr>\r\n" );
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document.write( "</TABLE>Make sure your calculator is in degree mode.\r<BR>\n" );
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document.write( "Here's one possible route if you wanted to use the law of sines<BR>\n" );
document.write( "sin(B)/b = sin(C)/c<BR>\n" );
document.write( "sin(46)/x = sin(90)/600<BR>\n" );
document.write( "600*sin(46) = x*sin(90)<BR>\n" );
document.write( "x = 600*sin(46)/sin(90)<BR>\n" );
document.write( "x = 431.60388020319<BR>\n" );
document.write( "x = 431.6\r<BR>\n" );
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document.write( "Keep in mind that sin(90) = 1, so this calculation isn't entirely new compared to option 1 mentioned earlier.\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>Approximately 431.6 miles</font><BR>\n" );
document.write( "Round this value however your teacher instructs.<BR>\n" );
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