document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=739430>Question 739430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many different triangles,if any, can be drawn with one 90 degree angle and side lengths of 5 cm. and 12 cm? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #451112 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=451112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:\r<BR>\n" );
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document.write( "one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" > degree angle and \r<BR>\n" );
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document.write( "side lengths of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5cm ALIGN=MIDDLE  ALT=\"5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12cm ALIGN=MIDDLE  ALT=\"12cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A right isosceles triangle has a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90-+45-+45 ALIGN=MIDDLE  ALT=\"90-+45-+45\"   DISABLED_style= \"max-width:90%; height:auto;\" > degree angles. \r<BR>\n" );
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document.write( "Another interesting right triangle is the 30-60-90 degree triangle. The ratio of this triangle's longest side to its shortest side is \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two ALIGN=MIDDLE  ALT=\"two\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one ALIGN=MIDDLE  ALT=\"one\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\" That is, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=longest ALIGN=MIDDLE  ALT=\"longest\"   DISABLED_style= \"max-width:90%; height:auto;\" > side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=twice ALIGN=MIDDLE  ALT=\"twice\"   DISABLED_style= \"max-width:90%; height:auto;\" > as long as the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=shortest ALIGN=MIDDLE  ALT=\"shortest\"   DISABLED_style= \"max-width:90%; height:auto;\" > side. \r<BR>\n" );
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document.write( " One of the most famous is the \"3, 4, 5 triangle.\"\r<BR>\n" );
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document.write( "However, the Pythagorean Theorem can help us to find third side if given side lengths of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5cm ALIGN=MIDDLE  ALT=\"5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+cm ALIGN=MIDDLE  ALT=\"12+cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "assume that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+cm ALIGN=MIDDLE  ALT=\"12+cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > is hypotenuse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5cm ALIGN=MIDDLE  ALT=\"5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > is leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E2=5%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"12%5E2=5%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144=25%2Bb%5E2 ALIGN=MIDDLE  ALT=\"144=25%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144-25=b%5E2 ALIGN=MIDDLE  ALT=\"144-25=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=119=b%5E2 ALIGN=MIDDLE  ALT=\"119=b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10.9087=b ALIGN=MIDDLE  ALT=\"10.9087=b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cannot ALIGN=MIDDLE  ALT=\"cannot\"   DISABLED_style= \"max-width:90%; height:auto;\" > be solution\r<BR>\n" );
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document.write( "let’s assume that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12cm ALIGN=MIDDLE  ALT=\"12cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > is leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5cm ALIGN=MIDDLE  ALT=\"5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > is leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=12%5E2%2B5%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=12%5E2%2B5%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=144%2B25 ALIGN=MIDDLE  ALT=\"c%5E2=144%2B25\"   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=169 ALIGN=MIDDLE  ALT=\"c%5E2=169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=13 ALIGN=MIDDLE  ALT=\"c=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" > solution\r<BR>\n" );
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document.write( "so, you can draw one triangle with one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" > degree angle and \r<BR>\n" );
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document.write( "sides lengths of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5cm ALIGN=MIDDLE  ALT=\"5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12cm ALIGN=MIDDLE  ALT=\"12cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13cm ALIGN=MIDDLE  ALT=\"13cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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