document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185801>Question 1185801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A kite is flying on 170 feet of string. How high is it above the ground if its height is 82 feet more than the horizontal distance from the person flying​ it? Assume the string is being released at ground level.\r<BR>\n" );
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document.write( "The kite is _____ feet above ground. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816646 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The information describes a right triangle with legs x (along the ground) and x+82 (the height above the ground) and a hypotenuse (the kite string) of 170.<br><BR>\n" );
document.write( "Use the Pythagorean Theorem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B82%29%5E2=170%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B82%29%5E2=170%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That gives a quadratic equation that you can solve to find x and then find the height.<br><BR>\n" );
document.write( "The numbers are large enough that solving by factoring, or even using the quadratic formula, is messy.  I would graph the two functions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B82%29%5E2%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B82%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=170%5E2 ALIGN=MIDDLE  ALT=\"170%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with a graphing calculator and find where they intersect.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-20%2C100%2C-5000%2C50000%2Cx%5E2%2B%28x%2B82%29%5E2%2C170%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-20%2C100%2C-5000%2C50000%2Cx%5E2%2B%28x%2B82%29%5E2%2C170%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The graphs intersect at x=72, so<br><BR>\n" );
document.write( "ANSWER: the height of the kite is 72+82=154 feet<br><BR>\n" );
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