document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177481>Question 1177481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The bearings of ships A and B from a port<BR>\n" );
document.write( "P are 225° and 116° respectively. Ship A is<BR>\n" );
document.write( "3.9 km from ship B on a bearing of 258º.<BR>\n" );
document.write( "Calculate the distance of ship A from P. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807161 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=807161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the following pictures should tell the story.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/040211.jpg\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/040212.jpg\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/040213.jpg\">\r<BR>\n" );
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document.write( "picture 1 shows the bearing from P to B and from P to A and from B to A.\r<BR>\n" );
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document.write( "that's 116 degrees and 225 degrees and 258 degrees respectively.\r<BR>\n" );
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document.write( "picture 2 shows the additional angles that results from the angles in picture 1.\r<BR>\n" );
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document.write( "angle FPB = 26 degrees because 116 degrees is equal to 90 degrees plus 26 degrees.\r<BR>\n" );
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document.write( "angle APB = 109 degrees because it's the difference between 225 degrees and 116 degrees.\r<BR>\n" );
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document.write( "angle PBG - 26 degrees because it is the alternate interior angle of angle FPB of the transversal PB between parallel lines PF and GB.\r<BR>\n" );
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document.write( "angle ABG = 12 degrees because it is is the diffence between a 258 degree angle and a 270 degree angle.  \r<BR>\n" );
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document.write( "picture 3 shows the triangle formed with all its interior angles.\r<BR>\n" );
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document.write( "because angle APB = 109 degrees and because angle PBA = 38 degrees, angle PAB has to be 33 degrees because the sum of the interior angles of a triangle = 180 degrees and 180 minus 109 minus 38 = 33 degrees.\r<BR>\n" );
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document.write( "picture 3 also shows the length of AB to be equal to 3.9 kilometers.\r<BR>\n" );
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document.write( "from picture 3, you can use the law of sines to get:\r<BR>\n" );
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document.write( "3.9 / sin(109) = PA / sin(38)\r<BR>\n" );
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document.write( "solve for PA to get:\r<BR>\n" );
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document.write( "PA = 3.9 * sin(38) / sin(109) = 2.539431605 km.\r<BR>\n" );
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document.write( "that should be your answer if i did this correctly.\r<BR>\n" );
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document.write( "the hard part was getting the angles right.<BR>\n" );
document.write( "once that was gone, it was a simple application of the law of sines.\r<BR>\n" );
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document.write( "3.9 km was the length of the side opposite angle 109.<BR>\n" );
document.write( "PA was the side opposite angle 38.<BR>\n" );
document.write( "we needed to find the length of side PA.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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