document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=747488>Question 747488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm stumped on this problem solving a system of equations with unknowns:<BR>\n" );
document.write( "A bridge across a river is built in the shape of a circular arc. The middle of the bridge is ten meters above the water, and twenty-seven meters from shore, the bridge is nine meters above the water. How wide is the river?\r<BR>\n" );
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document.write( "I've constructed the drawing with the center of the bridge passing thru the y-axis.  Here's the equations for the 4 points on the circle:\r<BR>\n" );
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document.write( "(1) (-h)^2 + (10-k)^2 = r^2<BR>\n" );
document.write( "(2) (w/2 - h)^2 + (-k)^2 = r^2<BR>\n" );
document.write( "(3) (-w/2 - h)^2 + (-k)^2 = r^2<BR>\n" );
document.write( "(4) (w/2-27-h)^2 + (9-k)^2 = r^2\r<BR>\n" );
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document.write( "Equation (1) h^2 + (10-k)^2 = r^2, since h=0, reduces to (10-k)^2 = r^2, or 10-k = r<BR>\n" );
document.write( "Equations (2) and (3) reduce to (w/2)^2 + k^2 = r^2, again since h=0<BR>\n" );
document.write( "Equation (4) reduces to (w/2-27)^2 + (9-k)^2 = r^2, again since h=0\r<BR>\n" );
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document.write( "I can't seem to solve this system of equations, I've multiplied these out several times and tried to group or eliminate common factors, but I'm missing something.  Can someone show me the steps?\r<BR>\n" );
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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 #454968 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem states\r<BR>\n" );
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document.write( "A bridge across a river is built in the shape of a circular arc. The middle of the bridge is ten meters above the water, and twenty-seven meters from shore, the bridge is nine meters above the water. How wide is the river? \r<BR>\n" );
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document.write( "The following web reference shows us the type of bridge we are dealing with:\r<BR>\n" );
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document.write( "http://en.wikipedia.org/wiki/File:MainStPano.jpg\r<BR>\n" );
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document.write( "looks like the river is 2*27 or 54 meters wide </SPAN>\n" );
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