document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082206>Question 1082206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A pilot takes off from Amber Island and flies for 150 km at 040T to BarterIsland where she unloads her first cargo. She intends to fly to Dream Island but a bad thunderstorm between Barter and Dream islands forces her to fly off course for 60 km to Crater Atoll on a bearing of 060T. She then turns on a bearing of 140T and flies for 100 km until she reaches Dream Island where she unloads her second cargo. She then takes off and flies 180 km on a bearing of 055T to Emerald Island. <BR>\n" );
document.write( "How many extra kilometres did she fly trying to avoid the storm? Round to the nearest km.\r<BR>\n" );
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document.write( "Monster of a question. I'm having trouble starting this question... I drew a graph but not sure on what to do next. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696942 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=696942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think i have it.\r<BR>\n" );
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document.write( "see the diagram.<BR>\n" );
document.write( "then look below for explanations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/052701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the points are labeled as:\r<BR>\n" );
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document.write( "barter island = A<BR>\n" );
document.write( "crater atoll = B<BR>\n" );
document.write( "dream island = C\r<BR>\n" );
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document.write( "the bearing from A to C is 60 degrees.<BR>\n" );
document.write( "that would be from barter island to crater atoll.\r<BR>\n" );
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document.write( "the bearing from C to B is 140 degrees.<BR>\n" );
document.write( "that would be from crater atoll to dream island.\r<BR>\n" );
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document.write( "the lines AC and CB are the route she took.<BR>\n" );
document.write( "the line AB is the route she should have taken.\r<BR>\n" );
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document.write( "draw a vertical line through point C.\r<BR>\n" );
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document.write( "since the bearing from C to B is 140, then the supplementary angle is 40 degrees as shown on the diagram.\r<BR>\n" );
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document.write( "draw a vertical line through point A.\r<BR>\n" );
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document.write( "the line AC forms a transversal of the vertical lines through point A and point C.\r<BR>\n" );
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document.write( "since both these lines are vertical, they are also parallel.\r<BR>\n" );
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document.write( "the 60 degrees shown at point A and the 60 degrees shown at point C are alternate interior angles of those parallel lines.\r<BR>\n" );
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document.write( "this makes then equal to each other.\r<BR>\n" );
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document.write( "within triangle ACB, you have just found the value of the angle at point C of the triangle.\r<BR>\n" );
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document.write( "that would be angle ACB which is equal to 100 degrees.\r<BR>\n" );
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document.write( "since you know the distances between A and C, and C and B, and you know the value of the included angle C of the triangle, you can use the law of cosines to find the distance between A and B.\r<BR>\n" );
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document.write( "using the law of cosines, you will find that the distance from A to B is equal to 125.23 kilometers.\r<BR>\n" );
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document.write( "that's the distance she should have flown.\r<BR>\n" );
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document.write( "the distance she actually flew is 160 km.\r<BR>\n" );
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document.write( "therefore she had to fly 160 - 125.23 = 34.77 kilometers out of her way.\r<BR>\n" );
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document.write( "now that you know the value of the line AB, you can use the law of sines or the law of cosines to find the value of angles A and B of the triangle.\r<BR>\n" );
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document.write( "the information shown on the diagram is all the information you needed to solve this problem as far as i can see.\r<BR>\n" );
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document.write( "the rest of the information was superfluous as far as i can tell.\r<BR>\n" );
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document.write( "the key was finding the angle at point C of the triangle.\r<BR>\n" );
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document.write( "from there, the distance between point A and B could be found using the law of cosines.\r<BR>\n" );
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document.write( "once you got that, the law of cosines or sines could be used to find the rest of the angles of the triangle.\r<BR>\n" );
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document.write( "this, i believe, is the solution to this problem.\r<BR>\n" );
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document.write( "here's a reference that i found useful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://cosmolearning.org/video-lectures/trigonometry-bearing-problems-4-examples/\" target = \"_blank\">https://cosmolearning.org/video-lectures/trigonometry-bearing-problems-4-examples/</a>\r<BR>\n" );
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document.write( "here's another one.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.youtube.com/watch?v=8rGa18-SJhA\" target = \"_blank\">https://www.youtube.com/watch?v=8rGa18-SJhA</a>\r<BR>\n" );
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document.write( "there's lots more on the web.<BR>\n" );
document.write( "just do a search for trigonometry bearing type problems and they should pop up.\r<BR>\n" );
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