document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=8055>Question 8055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is it possible to calculate the height from a given chord to a given arc, given that the only information available is the length of both the chord and the arc, I have been trying to calculate this for some time but it is in vain?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4445 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=4445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would say that it is possible, if you also have the radius of the circle or the angle subtended by the arc.\r<BR>\n" );
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document.write( "Here's one approach using the radius: A picture might help.\r<BR>\n" );
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document.write( "Draw a circle of radius r.<BR>\n" );
document.write( "Draw a chord of length c.<BR>\n" );
document.write( "Draw two radii from the circle center to the ends of the chord.<BR>\n" );
document.write( "Draw the radius from the circle center to the circumference, bisecting the chord.\r<BR>\n" );
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document.write( "Now, label the segment of the radius last drawn from the center to the chord as x.<BR>\n" );
document.write( "Label the remaining segment, the height you are looking for, as h.\r<BR>\n" );
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document.write( "Now, if drawn correctly, your diagram should show an isosceles triangle formed by two radii and the chord.  The isosceles triangle is bisected into two right-triangles with the radius (r) as their hypotenuses.\r<BR>\n" );
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document.write( "Using the Pythagorean theorem, you can find the length of segment x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%28r%5E2+-+%28c%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28r%5E2+-+%28c%2F2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Once you have found the length of segment x, the length of h is simply r - x.\r<BR>\n" );
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document.write( "So you have:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+r+-+sqrt%28r%5E2+-+c%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"h+=+r+-+sqrt%28r%5E2+-+c%5E2%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "You might see this written this way:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+r+-+%281%2F2%29sqrt%284r%5E2+-+c%5E2%29 ALIGN=MIDDLE  ALT=\"h+=+r+-+%281%2F2%29sqrt%284r%5E2+-+c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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