document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=674365>Question 674365</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am building a garden box in an Isosceles triangle shape. \r<BR>\n" );
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document.write( "The legs are 8 ft long, I don't know how to find the base length.  \r<BR>\n" );
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document.write( "can you please help. \r<BR>\n" );
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document.write( "thank you.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #419185 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=419185\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can't find the base length unless you know the vertex angle.<BR>\n" );
document.write( "that's the angle between the 2 equal sides.<BR>\n" );
document.write( "the 2 equal sides are 8 feet long each.<BR>\n" );
document.write( "the base will be any lengthy depending on the angle between the legs.<BR>\n" );
document.write( "it will range from 0 to 16<BR>\n" );
document.write( "it can't be equal to 0 because then your 2 legs will have collapsed against each other and there is no space left for the garden.<BR>\n" );
document.write( "it can't be 180 degrees because the legs will have collapsed against the base and you will not have any space for the garden.<BR>\n" );
document.write( "the angle has to be somewhere between 0 and 180 degrees but not equal to 0 or 180 degrees.<BR>\n" );
document.write( "assuming an angle of 90 degrees, then your isosceles triangle will have 2 legs of 8 feet each and a base of with a length of square root of (128)<BR>\n" );
document.write( "this is because by making the vertex angle 90 degrees, you created a right triangle with legs of 8 feet each and a hypotenuse as the base which means the pythagorean triangle formula can be used which is:<BR>\n" );
document.write( "a^2 + b^2 = c^2<BR>\n" );
document.write( "one of the legs if a and one of the legs is b and c is the base / hypotenuse of the isosceles triangle.<BR>\n" );
document.write( "you get 8^2 + 8^2 = c^2 which results in 64 + 64 = c^2 which results in 128 = c^2 which results in c = square root of 128.<BR>\n" );
document.write( "that's the length of the base, assuming the vertex angle is 90 degrees.<BR>\n" );
document.write( "that length is equal to 11.3237085 in decimal format.<BR>\n" );
document.write( "remember now, the vertex angle is the angle between the equal legs of the isosceles triangle.<BR>\n" );
document.write( "change the angle, and the length of the base changes.<BR>\n" );
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