document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136159>Question 1136159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two ships leave a harbor entrance at the same time. The first ship is traveling at a constant 10 miles per hour, while the second is traveling at a constant 14 miles per hour. If the angle between their courses is 123°, how far apart are they after 30 minutes? (Round your answer to the nearest whole number.) <BR>\n" );
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document.write( " =             mi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #753913 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=753913\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "*  *\r\n" );
document.write( " *     *\r\n" );
document.write( "  *         *       C\r\n" );
document.write( "   *             *\r\n" );
document.write( " 5  *                  *\r\n" );
document.write( "     *                      *          \r\n" );
document.write( "      *  123°                    *\r\n" );
document.write( "       ******************************\r\n" );
document.write( "                 7\r\n" );
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document.write( "After 30 minutes (0.5 hours), the ship that has a speed of 10 mph has traveled 5 miles and the ship that has a speed of 14 mph has traveled 7 miles.  Given is that the two ships are 123° apart.  So, this all forms a triangle. (See above.)  We are looking for C.<BR>\n" );
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document.write( "Use the law of cosines to find C:<BR>\n" );
document.write( "c² = a² + b² - 2ab(cos c)<BR>\n" );
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document.write( "Using our numbers:<BR>\n" );
document.write( "c² = 5² + 7² - 2(5)(7)(cos 123°)<BR>\n" );
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document.write( "c² = 25 + 49 - 70(cos 123°)<BR>\n" );
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document.write( "c² = 74 - 70(cos 123°)<BR>\n" );
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document.write( "c² = 74 - 70(-0.54464)<BR>\n" );
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document.write( "c² = 74 + 38.1248<BR>\n" );
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document.write( "c² = 112.1248<BR>\n" );
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document.write( "c = 10.5889<BR>\n" );
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document.write( "The two ships are 10.5889 miles apart after 30 minutes. </SPAN>\n" );
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