document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70763>Question 70763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, \r<BR>\n" );
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document.write( "I need help with this: If the hypotenuse of a right triangle is 10 and one leg is 5, what is the length of the other leg?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50551 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=50551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Are you familiar with the \"Pythagorean theorem\"?<BR>\n" );
document.write( "This is the theorem that shows the relationship among the three sides of a right triangle. In algebra, it looks like this:<BR>\n" );
document.write( "<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;\" > where:<BR>\n" );
document.write( "c is the length of the hypotenuse.<BR>\n" );
document.write( "a and b are the lengths of the two legs.<BR>\n" );
document.write( "So, if you are given the lengths of any two sides of a right triangle, you can find the length of the third side using the Pythagorean theorem.<BR>\n" );
document.write( "Let's apply this to your problem.<BR>\n" );
document.write( "The hypotenuse is given as 10 units, so c = 10<BR>\n" );
document.write( "One leg is given as 5 units, so a  = 5<BR>\n" );
document.write( "Now substitute these values of c and a into the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2+=+5%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"10%5E2+=+5%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100+=+25+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"100+=+25+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 25 from both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75+=+b%5E2 ALIGN=MIDDLE  ALT=\"75+=+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+sqrt%2875%29 ALIGN=MIDDLE  ALT=\"b+=+sqrt%2875%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > You really get two values when you take the square root of a number, a positive and a negative.  But, because we are finding the length of a side of the triangle and length is a positive quantity, we can ignore the negative value.<BR>\n" );
document.write( "The length of the other leg is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2875%29+=+5sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%2875%29+=+5sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >units </SPAN>\n" );
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