document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199738>Question 199738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carpenters and builders will sometimes measure 3 ft from a corner along one wall and 4 ft along the other, then check that it's 5 ft between the 2 points. If it is, the walls are \"square\", at right angles.\r<BR>\n" );
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document.write( "If the two short sides of a building are 3 and 4 how would you show carefully that you used the Pythagorean theorem to calculate the diagonal as 5?<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 #150116 by </B><A HREF=/tutors/aboutme.mpl?userid=tutor_paul><B>tutor_paul(519)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutor_paul><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=tutor_paul><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=150116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Pythagorean Theorem is wriiten as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Where:<BR>\n" );
document.write( "a = one side of a right triangle<BR>\n" );
document.write( "b = the other side of a right triangle<BR>\n" );
document.write( "c = the hypoteneuse (diagonal) of a right trianagle\r<BR>\n" );
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document.write( "Note that this equation applies only to right triangles - which is a triangle which has one angle of 90 degrees. The hypoteneuse is the side of the triangle opposite this 90 degree angle.\r<BR>\n" );
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document.write( "So back to the problem... the goal is to make sure that the walls of the building are \"square.\" That means that they form a 90 degree angle. So let's apply the pythagorean theorem to prove that if the 2 walls are length 3 and 4 respectively, the diagonal is 5.\r<BR>\n" );
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document.write( "Pythagorean Theorem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute in your given values:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2%2B4%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"3%5E2%2B4%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B16=c%5E2 ALIGN=MIDDLE  ALT=\"9%2B16=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=25 ALIGN=MIDDLE  ALT=\"c%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28c%5E2%29=sqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%28c%5E2%29=sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=5%29 ALIGN=MIDDLE  ALT=\"highlight%28c=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So you have proven that the diagonal is 5. Thus from the given information in the problem, you also know that the walls form a right angle.\r<BR>\n" );
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document.write( "============<BR>\n" );
document.write( "Good Luck,<BR>\n" );
document.write( "tutor_paul@yahoo.com\r<BR>\n" );
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