document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=632284>Question 632284</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An arch in the form of a semiellipse is 64 ft wide at the base and has a height of 30 ft.<BR>\n" );
document.write( "How high is the arch at a width of 20 ft from the center of the base? Round your answer<BR>\n" );
document.write( "to the nearest tenth.<BR>\n" );
document.write( "10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #398197 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=398197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An arch in the form of a semiellipse is 64 ft wide at the base and has a height of 30 ft.<BR>\n" );
document.write( "How high is the arch at a width of 20 ft from the center of the base? Round your answer<BR>\n" );
document.write( "to the nearest tenth.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Given problem is finding the equation of an ellipse with horizontal major axis and center at (0,0), then plugging in given x to find y.<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%2B1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b<BR>\n" );
document.write( "a=32 ft (horizontal distance from center to vertex)<BR>\n" );
document.write( "a^2=32^2=1024<BR>\n" );
document.write( "b=30 ft (vertical distance from center to top of the arch)<BR>\n" );
document.write( "b^2=900<BR>\n" );
document.write( "equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F1024%2By%5E2%2F900=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F1024%2By%5E2%2F900=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solve for y when x=20 ft from center<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5E2%2F1024%2By%5E2%2F900=1 ALIGN=MIDDLE  ALT=\"20%5E2%2F1024%2By%5E2%2F900=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y^2/900=1-20^2/1024=1-400/1024=1-.391=0.609<BR>\n" );
document.write( "y^2=.609*900=548.44<BR>\n" );
document.write( "y=&#8730;548.44<BR>\n" );
document.write( "y&#8776;23.4<BR>\n" );
document.write( "Height of the arch at a width of 20 ft from the center of the base&#8776;23.4 ft </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );