document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089471>Question 1089471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man travels 5 km due north from his starting point and then travels a further 8 km in a straight line in the direction 30 degrees east of north.How far is he from his starting position ?<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 #703814 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=703814\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you could solve this by creating right triangles, or you can solve using the following formula:\r<BR>\n" );
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document.write( "b^2 = a^2 + c^2 - 2 * a * c * cos(B)\r<BR>\n" );
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document.write( "this, i believe, is called the law of cosines.\r<BR>\n" );
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document.write( "here's a reference:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.mathwarehouse.com/trigonometry/law-of-cosines-formula-examples.php\" target = \"_blank\">http://www.mathwarehouse.com/trigonometry/law-of-cosines-formula-examples.php</a>\r<BR>\n" );
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document.write( "here's a picture of my worksheet.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/080201.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the triangle is labeled ABC.\r<BR>\n" );
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document.write( "A is the starting point.<BR>\n" );
document.write( "B is the point 5 km due north.<BR>\n" );
document.write( "C is the point 8 km due 30 degrees east of north.\r<BR>\n" );
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document.write( "angle B in the triangle is 150 degrees, since it is supplementary to the 30 degree angle.\r<BR>\n" );
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document.write( "side a is opposite angle A of the triangle.<BR>\n" );
document.write( "side b is opposite angle B of the triangle.<BR>\n" );
document.write( "sice c is opposite angle C of the triangle.\r<BR>\n" );
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document.write( "this fits the law of cosines since you are looking for the side opposite the known angle and you have the measure of the side adjacent to that angle.\r<BR>\n" );
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document.write( "the worksheet has the details of the calculations.\r<BR>\n" );
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document.write( "cos(150) is equal to -.8660254038\r<BR>\n" );
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document.write( "the rest is just solving the equation.\r<BR>\n" );
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document.write( "any questions, give me a shout.\r<BR>\n" );
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document.write( "otherwise, i believe you have all that you need.\r<BR>\n" );
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document.write( "another law that is sometimes useful is the law of sines.\r<BR>\n" );
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document.write( "a reference to that can be found here:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.mathwarehouse.com/trigonometry/law-of-sines/formula-and-practice-problems.php\" target = \"_blank\">http://www.mathwarehouse.com/trigonometry/law-of-sines/formula-and-practice-problems.php</a>\r<BR>\n" );
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