document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118091>Question 118091</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the length x in the triangle. Express your answer in simplified radical form. Side 1=10. Side 2=8. Side 3=x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86162 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=86162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming that the triangle is a right triangle and that side 3 is the hypotenuse.\r<BR>\n" );
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document.write( "We basically have this triangle set up:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-0.5%2C2%2C-0.5%2C3.2%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C3%29%2C%0D%0Aline%280%2C3%2C2%2C0%29%2C%0D%0Aline%282%2C0%2C0%2C0%29%2C%0D%0Alocate%28-0.2%2C1.5%2C10%29%2C%0D%0Alocate%281%2C-0.2%2C8%29%2C%0D%0Alocate%281%2C2%2Cx%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we can see that the triangle has legs of 10 and 8 with a hypotenuse of x, we can use Pythagoreans theorem to find the unknown side.\r<BR>\n" );
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document.write( "Pythagoreans theorem:\r<BR>\n" );
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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;\" > where a and b are the legs of the triangle and c is the hypotenuse\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2%2B8%5E2=x%5E2 ALIGN=MIDDLE  ALT=\"10%5E2%2B8%5E2=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plug in a=10, b=8, and c=x. Now lets solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+0+0+%2B+6+4+=++x++%5E+2 ALIGN=MIDDLE  ALT=\"1+0+0+%2B+6+4+=++x++%5E+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square each individual term\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+6+4+=++x++%5E+2 ALIGN=MIDDLE  ALT=\"1+6+4+=++x++%5E+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+q+r+t+%28+1+6+4+%29+=+s+q+r+t+%28++x++%5E+2+%29 ALIGN=MIDDLE  ALT=\"s+q+r+t+%28+1+6+4+%29+=+s+q+r+t+%28++x++%5E+2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2841%29=x ALIGN=MIDDLE  ALT=\"2%2Asqrt%2841%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root\r<BR>\n" );
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document.write( "Which approximates to...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.8062484748657=x ALIGN=MIDDLE  ALT=\"12.8062484748657=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12.8062484748657 ALIGN=MIDDLE  ALT=\"x=12.8062484748657\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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