document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72631>Question 72631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem,  where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides’ measurements are 3 feet and 4 feet </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51932 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Pythagorean theorem says that the sum of the squares of the two legs (short sides) of<BR>\n" );
document.write( "a right triangle are equal to the square of the long side (the hypotenuse). In equation<BR>\n" );
document.write( "form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which \"a\" and \"b\" represent the legs and \"c\" represents the hypotenuse.  For this problem<BR>\n" );
document.write( "we know that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+3 ALIGN=MIDDLE  ALT=\"a+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "and:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+4 ALIGN=MIDDLE  ALT=\"b+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute these values into the equation for the Pythagorean theorem and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+%2B+4%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"3%5E2+%2B+4%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now do the calculations. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+=+3%2A3+=+9 ALIGN=MIDDLE  ALT=\"3%5E2+=+3%2A3+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2+=+4%2A4+=+16 ALIGN=MIDDLE  ALT=\"4%5E2+=+4%2A4+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute <BR>\n" );
document.write( "these values to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%2B+16+=+c%5E2 ALIGN=MIDDLE  ALT=\"9+%2B+16+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The addition on the left side gives you:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+=+c%5E2 ALIGN=MIDDLE  ALT=\"25+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and you now take the square root of both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+5 ALIGN=MIDDLE  ALT=\"c+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the hypotenuse or long side of this right triangle is 5 units long.<BR>\n" );
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document.write( "Just for information, any builder knows about the 3 - 4 - 5 triangle.  He or she uses it<BR>\n" );
document.write( "to make sure that walls are at right angles. They do this by measuring down one wall 3 feet <BR>\n" );
document.write( "and marking that spot. They then measure down the perpendicular wall 4 feet and marking<BR>\n" );
document.write( "that spot also.  Then they measure the slant distance between the two spots.  If that <BR>\n" );
document.write( "distance isn't 5 feet exactly, then they know the walls are not really perpendicular to each<BR>\n" );
document.write( "other and they will have to adjust the walls until they get the distance between the 3-foot<BR>\n" );
document.write( "and 4-foot marks to be exactly 5 feet.  Sometimes geometry really is helpful in the real<BR>\n" );
document.write( "world.<BR>\n" );
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document.write( "Remember this one.  Someday you're going to want to fence something in and you can use<BR>\n" );
document.write( "this triangle to make sure the corners of your fence lines are a right angles to each other<BR>\n" );
document.write( "(even if you can't remember what the Pythagorean theorem is).<BR>\n" );
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document.write( "Hope this helps you to understand the Pythagorean theorem a little better.<BR>\n" );
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