document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180870>Question 1180870</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Triangle ABC is an isosceles right triangle with <C as the right angle.<BR>\n" );
document.write( "1. If a=5 cm, find c.<BR>\n" );
document.write( "2. If b=8 cm, find c.<BR>\n" );
document.write( "3. If b=12.5 cm, find c.\r<BR>\n" );
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document.write( "Triangle GMA is a 30°-60°-90° triangle.<BR>\n" );
document.write( "4. If m=26 cm, find a and g.<BR>\n" );
document.write( "5. If a=30 cm, find m and g.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810663 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=810663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Triangle ABC is an isosceles right triangle with \r<BR>\n" );
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document.write( "1. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5cm ALIGN=MIDDLE  ALT=\"a=5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "since triangle ABC is an isosceles right triangle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b=5cm ALIGN=MIDDLE  ALT=\"a=b=5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28%285cm%29%5E2%2B%285cm%29%5E2%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28%285cm%29%5E2%2B%285cm%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%2825cm%5E2%2B25cm%5E2%29%29 ALIGN=MIDDLE  ALT=\"c=sqrt%2825cm%5E2%2B25cm%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%2850cm%5E2%29 ALIGN=MIDDLE  ALT=\"c=sqrt%2850cm%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=7.07cm ALIGN=MIDDLE  ALT=\"c=7.07cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.<BR>\n" );
document.write( " If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=8cm ALIGN=MIDDLE  ALT=\"b=8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   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=a=8cm ALIGN=MIDDLE  ALT=\"a=8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28%288cm%29%5E2%2B%288cm%29%5E2%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28%288cm%29%5E2%2B%288cm%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%2864cm%5E2%2B64cm%5E2%29%29 ALIGN=MIDDLE  ALT=\"c=sqrt%2864cm%5E2%2B64cm%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28128cm%5E2%29%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28128cm%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=11.31cm ALIGN=MIDDLE  ALT=\"c=11.31cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3. <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=12.5cm ALIGN=MIDDLE  ALT=\"b=12.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=12.5cm ALIGN=MIDDLE  ALT=\"a=12.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28%2812.5cm%29%5E2%2B%2812.5cm%29%5E2%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28%2812.5cm%29%5E2%2B%2812.5cm%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28156.5cm%5E2%2B156.5cm%5E2%29%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28156.5cm%5E2%2B156.5cm%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28312.5cm%5E2%29%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28312.5cm%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=17.68cm ALIGN=MIDDLE  ALT=\"c=17.68cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Triangle GMA is a 30°-60°-90° triangle.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"https://ibb.co/nLwKzRb\"><IMG STYLE=\"max-width:80%;\" src=\"https://i.ibb.co/nLwKzRb/triangle.png\" alt=\"triangle\" border=\"0\"></a>\r<BR>\n" );
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document.write( "if GMA is a 30°-60°-90° triangle, then <BR>\n" );
document.write( "The shorter leg, which is opposite to the 30- degree angle, is labeled as<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x ALIGN=MIDDLE  ALT=\"+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The hypotenuse, which is opposite to the 90-degree angle, is twice the shorter leg length (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "The longer leg, which is opposite to the 60-degree angle, is equal to the shorter leg’s product and the square root of three (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xsqrt%283%29 ALIGN=MIDDLE  ALT=\"xsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "in your case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2x ALIGN=MIDDLE  ALT=\"m=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  shorter leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=x ALIGN=MIDDLE  ALT=\"g=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and longer leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=xsqrt%283%29 ALIGN=MIDDLE  ALT=\"a=xsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4. <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=26cm ALIGN=MIDDLE  ALT=\"m=26cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find <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=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "if hypotenuse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=26cm ALIGN=MIDDLE  ALT=\"m=26cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=26cm ALIGN=MIDDLE  ALT=\"2x=26cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13cm ALIGN=MIDDLE  ALT=\"x=13cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then shorter leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=13cm ALIGN=MIDDLE  ALT=\"g=13cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and longer leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=13cm%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"a=13cm%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, check<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2=a%5E2%2Bg%5E2 ALIGN=MIDDLE  ALT=\"m%5E2=a%5E2%2Bg%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826cm%29%5E2=%2813cm%2Asqrt%283%29%29%5E2%2B%2813cm%29%5E2 ALIGN=MIDDLE  ALT=\"%2826cm%29%5E2=%2813cm%2Asqrt%283%29%29%5E2%2B%2813cm%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=676cm%5E2=169cm%5E2%2A3%2B169cm%5E2 ALIGN=MIDDLE  ALT=\"676cm%5E2=169cm%5E2%2A3%2B169cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=676cm%5E2=507cm%5E2%2B169cm%5E2 ALIGN=MIDDLE  ALT=\"676cm%5E2=507cm%5E2%2B169cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=676cm%5E2=676cm%5E2 ALIGN=MIDDLE  ALT=\"676cm%5E2=676cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5. <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=30cm ALIGN=MIDDLE  ALT=\"a=30cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=30cm ALIGN=MIDDLE  ALT=\"a=30cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xsqrt%2813%29=30 ALIGN=MIDDLE  ALT=\"xsqrt%2813%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=30%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"x=30%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=2%2A%2830%2Fsqrt%283%29%29=60%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"2x=2%2A%2830%2Fsqrt%283%29%29=60%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=60%2Fsqrt%283%29cm ALIGN=MIDDLE  ALT=\"m=60%2Fsqrt%283%29cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%2860sqrt%283%29%2F3%29cm ALIGN=MIDDLE  ALT=\"m=%2860sqrt%283%29%2F3%29cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=20sqrt%283%29cm ALIGN=MIDDLE  ALT=\"m=20sqrt%283%29cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=%2830%2Fsqrt%283%29%29cm ALIGN=MIDDLE  ALT=\"g=%2830%2Fsqrt%283%29%29cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=%28%2830sqrt%283%29%29%2F3%29cm ALIGN=MIDDLE  ALT=\"g=%28%2830sqrt%283%29%29%2F3%29cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=10sqrt%283%29cm ALIGN=MIDDLE  ALT=\"g=10sqrt%283%29cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2=a%5E2%2Bg%5E2 ALIGN=MIDDLE  ALT=\"m%5E2=a%5E2%2Bg%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820sqrt%283%29cm%29%5E2=%2830cm%29%5E2%2B%2810sqrt%283%29cm%29%5E2 ALIGN=MIDDLE  ALT=\"%2820sqrt%283%29cm%29%5E2=%2830cm%29%5E2%2B%2810sqrt%283%29cm%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%2A3cm%5E2=900cm%5E2%2B100%2A3cm%5E2 ALIGN=MIDDLE  ALT=\"400%2A3cm%5E2=900cm%5E2%2B100%2A3cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200cm%5E2=900cm%5E2%2B300cm%5E2 ALIGN=MIDDLE  ALT=\"1200cm%5E2=900cm%5E2%2B300cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200cm%5E2=1200cm%5E2 ALIGN=MIDDLE  ALT=\"1200cm%5E2=1200cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );