document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912080>Question 912080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A kite 100ft above the ground moves horizontally at a speed of 5ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200ft of string have been let out? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553594 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=553594\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A kite 100ft above the ground moves horizontally at a speed of 5ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200ft of string have been let out?<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "It's a right triangle.<BR>\n" );
document.write( "sin(A) = 100/200 --> A = pi/6<BR>\n" );
document.write( "sec^2(A) = 4/3<BR>\n" );
document.write( "------<BR>\n" );
document.write( "x = horizontal distance = sqrt(200^2 - 100^2) = 100sqrt(3)<BR>\n" );
document.write( "tan(A) = 100/x<BR>\n" );
document.write( "sec^2(A)*(dA/dt) = -1*100/x^2*(dx/dt) = -(100/30000)*5<BR>\n" );
document.write( "dA/dt = -(100*(3/4)/(30000))*(5)<BR>\n" );
document.write( "dA/dt = -375/30000<BR>\n" );
document.write( "= -0.0125 rad/sec<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );