document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395514>Question 395514</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At what time(s) between 5 and 6 o'clock will the hour and the minute hands be at right angles? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280684 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=280684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can assign 12:00 as 0 degrees, 1:00 as 30 degrees, etc.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If the time is 5 hours and x minutes after 5:00, then the angle formed by the minute hand is (x/60)(360) = 6x (degrees). For each minute after 5, the hour hand moves 1/2 degree, so the hour hand has an angle of 150 + x/2. The angle between them is 90 degrees, so\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%28150+%2B+x%2F2%29+-+6x%29+=+90 ALIGN=MIDDLE  ALT=\"abs%28%28150+%2B+x%2F2%29+-+6x%29+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28150+-+11x%2F2%29+=+90 ALIGN=MIDDLE  ALT=\"abs%28150+-+11x%2F2%29+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150+-+11x%2F2+=+90 ALIGN=MIDDLE  ALT=\"150+-+11x%2F2+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150+-+11x%2F2+=+-90 ALIGN=MIDDLE  ALT=\"150+-+11x%2F2+=+-90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+120%2F11+=+10.909 ALIGN=MIDDLE  ALT=\"x+=+120%2F11+=+10.909\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+480%2F11+=+43.636 ALIGN=MIDDLE  ALT=\"x+=+480%2F11+=+43.636\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore the angle between the hands is 90 at roughly 5:11 and 5:44. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );