document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548679>Question 548679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> this was on my home work<BR>\n" );
document.write( "jason,kevin,and randy found themselves far apart when they stoped for lunch while working in a field.jason could see kevin,then turn through 75degrees and see randy.kevin could see randy,the turn 50 degrees and see jason.randy could see jason,then turn through 55 degree and see kevin.which two were farthest apart ? <BR>\n" );
document.write( "a: kevin and randy<BR>\n" );
document.write( "B: jason and kevin<BR>\n" );
document.write( "C:randy and jason<BR>\n" );
document.write( "D: kevin and randy were the same distance apart as randy and jason\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357193 by </B><A HREF=/tutors/aboutme.mpl?userid=skarout><B>skarout(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=skarout><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=skarout><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=357193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let us give a name for each point where each person stand:<BR>\n" );
document.write( "J for Jason / K for Kevin / R for Randy.<BR>\n" );
document.write( "Let we draw the triangle where Jason-Kevin ^ Jason-Randi angle 75deg<BR>\n" );
document.write( "so JK^JR = 75deg<BR>\n" );
document.write( "same for:<BR>\n" );
document.write( "KJ^KR = 50deg<BR>\n" );
document.write( "RK^RJ = 55 deg\r<BR>\n" );
document.write( "\n" );
document.write( "having this triangle RJK, draw perpenducular lines from each point to each opposit side, it will divide each side to two segment.\r<BR>\n" );
document.write( "\n" );
document.write( "so<BR>\n" );
document.write( "JK = JR*Cos(75) + KR*Cos(50) (1)<BR>\n" );
document.write( "JR = JK*cos(75) + KR*Cos(55) (2)<BR>\n" );
document.write( "KR = JK*Cos(50) + JR*Cos(55) (3)\r<BR>\n" );
document.write( "\n" );
document.write( "substitute for KR in JK formulas (3) in (1):<BR>\n" );
document.write( "JK = JR*Cos(75) + [JK*Cos(50) + JR*Cos(55)]*Cos(50)<BR>\n" );
document.write( "JK = JR*Cos(75) + JK*Cos(50)*Cos(50) + JR*Cos(55)*Cos(50)<BR>\n" );
document.write( "this will lead to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=JK=%28%28Cos%2875%29+%2B+Cos%2855%29%2ACos%2850%29%29%2F%281-Cos%2850%29%5E2%29%29%2AJR ALIGN=MIDDLE  ALT=\"JK=%28%28Cos%2875%29+%2B+Cos%2855%29%2ACos%2850%29%29%2F%281-Cos%2850%29%5E2%29%29%2AJR\"   DISABLED_style= \"max-width:90%; height:auto;\" > (4)\r<BR>\n" );
document.write( "\n" );
document.write( "OR\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=JK=%28%28Cos%2875%29+%2B+Cos%2855%29%2ACos%2850%29%29%2F%28Sin%2850%29%5E2%29%29%2AJR ALIGN=MIDDLE  ALT=\"JK=%28%28Cos%2875%29+%2B+Cos%2855%29%2ACos%2850%29%29%2F%28Sin%2850%29%5E2%29%29%2AJR\"   DISABLED_style= \"max-width:90%; height:auto;\" > (5)\r<BR>\n" );
document.write( "\n" );
document.write( "OR for JR:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=JR=+%28Sin%2850%29%5E2%2F%28Cos%2875%29+%2B+Cos%2855%29%2ACos%2850%29%29%29%2AJK ALIGN=MIDDLE  ALT=\"JR=+%28Sin%2850%29%5E2%2F%28Cos%2875%29+%2B+Cos%2855%29%2ACos%2850%29%29%29%2AJK\"   DISABLED_style= \"max-width:90%; height:auto;\" > (6)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the same way substituting JR in JK formulas (2) in (1) will have:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=JK=%28%28Cos%2850%29%2BCos%2855%29%2ACos%2875%29%29%2F%28Sin%2875%29%5E2%29%29%2AKR ALIGN=MIDDLE  ALT=\"JK=%28%28Cos%2850%29%2BCos%2855%29%2ACos%2875%29%29%2F%28Sin%2875%29%5E2%29%29%2AKR\"   DISABLED_style= \"max-width:90%; height:auto;\" > (7)\r<BR>\n" );
document.write( "\n" );
document.write( "OR\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=KR=%28Sin%2875%29%5E2%2F%28Cos%2850%29%2BCos%2855%29%2ACos%2875%29%29%29%2AJK ALIGN=MIDDLE  ALT=\"KR=%28Sin%2875%29%5E2%2F%28Cos%2850%29%2BCos%2855%29%2ACos%2875%29%29%29%2AJK\"   DISABLED_style= \"max-width:90%; height:auto;\" > (8)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Calculate the result for (6) and (8):\r<BR>\n" );
document.write( "\n" );
document.write( "formula (6) will give: JR = 0.93516 * JK this means that: JR < JK<BR>\n" );
document.write( "and (8) will give:     KR = 1.17917 * JK this means that: JK < KR\r<BR>\n" );
document.write( "\n" );
document.write( "so we have JR < JK < KR\r<BR>\n" );
document.write( "\n" );
document.write( "so farthest two points are KR\r<BR>\n" );
document.write( "\n" );
document.write( "this means that Kaven and Randy are the farthest apart.\r<BR>\n" );
document.write( "\n" );
document.write( "so answer is \"a\"\r<BR>\n" );
document.write( "\n" );
document.write( "thanks. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );