document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328202>Question 328202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jan is flying on a triangular course at 320 mi/h. She flies due east for two hours and then turns right through a 65 degree angle. How long after turning will she be exactly southeast of where she started?<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 #235068 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are various ways to go about this one. Here is one method.\r<BR>\n" );
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document.write( "From where she makes her 65 degree turn, extend a line straight out, then connect it to the point where she intersects the southwest line. \r<BR>\n" );
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document.write( "This forms a right triangle. Draw a line from the intersection point back to where she turned. This forms another triangle.\r<BR>\n" );
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document.write( "Let the distance extended out from where she turned be x and the distance from there to the intersection point be 640+x (because southeast is 45 degrees from the origin)\r<BR>\n" );
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document.write( "The distance she flies is 320t.\r<BR>\n" );
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document.write( "Now, we can build two triangles and solve for t and x. t is what we really need.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2825%29=x%2F320t ALIGN=MIDDLE  ALT=\"sin%2825%29=x%2F320t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28640%2Bx%29%5E2=%28320t%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28640%2Bx%29%5E2=%28320t%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....[2]\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=320t%2Asin%2825%29 ALIGN=MIDDLE  ALT=\"x=320t%2Asin%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....[3]\r<BR>\n" );
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document.write( "Sub [3] into [2] and solve for t.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28320t%2Asin%2825%29%29%5E2%2B%28640%2B%28320t%2Asin%2825%29%29%29%5E2=%28320t%29%5E2 ALIGN=MIDDLE  ALT=\"%28320t%2Asin%2825%29%29%5E2%2B%28640%2B%28320t%2Asin%2825%29%29%29%5E2=%28320t%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=204800sin%5E2%2825%29%2At%5E2%2B409600sin%2825%29t%2B409600=102400t%5E2 ALIGN=MIDDLE  ALT=\"204800sin%5E2%2825%29%2At%5E2%2B409600sin%2825%29t%2B409600=102400t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is a quadratic to solve for t.\r<BR>\n" );
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document.write( "Doing so, gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4.13 ALIGN=MIDDLE  ALT=\"t=4.13\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours.\r<BR>\n" );
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document.write( "The other solution is extraneous. </SPAN>\n" );
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