document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185237>Question 1185237</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the longer leg of a 30-60-90 triangle if its\r<BR>\n" );
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document.write( "hypotenuse is 2√3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816030 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the hypotenuse is 2 * sqrt(3).\r<BR>\n" );
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document.write( "the angles are 30, 60, and 90.\r<BR>\n" );
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document.write( "the  trigonometric functions are:\r<BR>\n" );
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document.write( "sin(30) = 1/2\r<BR>\n" );
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document.write( "sin(60) = sqrt(2)/3\r<BR>\n" );
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document.write( "hypotenuse is equal to sqrt((1/2)^2 + (sqrt(3)/2)^2) = 1\r<BR>\n" );
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document.write( "if the hypotenuse is equal to 2*sqrt(3), then all sides need to be multiplied by 2*sqrt(3).\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "hypotenuse = 1 * 2 * sqrt(30 = 2 * sqrt(30\r<BR>\n" );
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document.write( "side opposite 30 degree angle = 1/2 * 2 * sqrt(30 = sqrt(3)\r<BR>\n" );
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document.write( "side opposite 60 degree angle = sqrt(3)/2 * 2 * sqrt)30 = 3\r<BR>\n" );
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document.write( "the sum of the sides squared must be equal to the the square of the hypotenuse.\r<BR>\n" );
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document.write( "(2 * sqrt(3))^2 = sqrt(3)^2 + 3^2.<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "12 = 3 + 9 which becomes:<BR>\n" );
document.write( "12 = 12\r<BR>\n" );
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document.write( "this confirms the new sizes of the legs are correct when the hypotenuse is equal to 2 * sqrt(3).\r<BR>\n" );
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document.write( "the longest leg would be the leg whose length is equal to 3.\r<BR>\n" );
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document.write( "here's a reference on 30, 60, 90 degree triangle.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://blog.prepscholar.com/30-60-90-triangle-ratio-formula\" target = \"_blank\">https://blog.prepscholar.com/30-60-90-triangle-ratio-formula</a>\r<BR>\n" );
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document.write( "they get the same result a different way.\r<BR>\n" );
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document.write( "one of their examples is the  triangle whose hypotenuse is 2 * sqrt(3).\r<BR>\n" );
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document.write( "you coculd have gotten the answer either way.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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