document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208678>Question 208678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If one side of a right triangle is 3 inches and the hypotenuse is 4 inches, how long is the other side? I need help with the formula and solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157821 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=157821\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The 3 sides of <b>every</b> right triangle must fit the equation from the Pythagorean Theorem: <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;\" >. The only \"trick\" is to understand that the hypotenuse, since it is always the longest side, must be the \"c\" in the equation. (It makes no difference which leg is \"a\" and which leg is \"b\".)<br><BR>\n" );
document.write( "So we'll make the 3-inch leg \"a\" and the hypotenuse must be \"c\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%5E2+%2B+b%5E2+=+%284%29%5E2 ALIGN=MIDDLE  ALT=\"%283%29%5E2+%2B+b%5E2+=+%284%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we just solve this to find \"b\", the other leg. Start by simplifying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%2B+b%5E2+=+16 ALIGN=MIDDLE  ALT=\"9+%2B+b%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 9 from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+7 ALIGN=MIDDLE  ALT=\"b%5E2+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the square root of both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%5E2%29+=+sqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%28b%5E2%29+=+sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28b%29+=+sqrt%287%29 ALIGN=MIDDLE  ALT=\"abs%28b%29+=+sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+sqrt%287%29 ALIGN=MIDDLE  ALT=\"b+=+sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-sqrt%287%29 ALIGN=MIDDLE  ALT=\"b+=+-sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since \"b\" represents the side of a triangle, we reject the negative solution. So the answer is that the third side of the triangle has a length of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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