document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190010>Question 1190010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two friends say ‘goodbye’ as they leave the school heading home in different directions. Jayshan<BR>\n" );
document.write( "walks 180 metres in one direction and Aneesa runs an unknown number of metres in another direction<BR>\n" );
document.write( "such that the angle between the friends is 72°. If the distance between the two friends is 485 metres,<BR>\n" );
document.write( "then calculate how far Aneesa ran, rounding your answer to the nearest metre.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821603 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=821603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = how far Aneesa ran, in meters<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/cPkNmSu.png\"><BR>\n" );
document.write( "Drawing is not to scale\r<BR>\n" );
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document.write( "Use the law of cosines to solve for x.<BR>\n" );
document.write( "c^2 = a^2+b^2 - 2*a*b*cos(C)<BR>\n" );
document.write( "485^2 = 180^2+x^2 - 2*180*x*cos(72)<BR>\n" );
document.write( "485^2 = 180^2+x^2 - 2*180*x*0.30901699437494<BR>\n" );
document.write( "235225 = 32400+x^2 - 111.246117974979x<BR>\n" );
document.write( "0 = 32400+x^2 - 111.246117974979x - 235225<BR>\n" );
document.write( "x^2 - 111.246117974979x - 202825 = 0\r<BR>\n" );
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document.write( "From here, you'll need the quadratic formula. I'll skip those steps but you should get the following roots:<BR>\n" );
document.write( "x = -398.16<BR>\n" );
document.write( "x = 509.41<BR>\n" );
document.write( "both of which are approximate\r<BR>\n" );
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document.write( "We ignore the negative root. It doesn't make sense to have Aneesa run a negative distance.\r<BR>\n" );
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document.write( "The only practical solution here is roughly x = 509.41<BR>\n" );
document.write( "This rounds to 509\r<BR>\n" );
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document.write( "Answer: 509 meters<BR>\n" );
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