document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=661169>Question 661169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have a right triangle with a 90 degree angle and a hypotenuse of 18 i need to find the two short side lengths pleassse (: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #411546 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=411546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you need to know the length of one of the sides.<BR>\n" );
document.write( "otherwise, you will have 1 equation in 2 unknowns which can't be solved for a single value but can be solved for a multiple number of values if you assume a number for one for one of them.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "triangle is a right triangle with a hypotenuse of 18.<BR>\n" );
document.write( "the pythatogean formula says that a^2 + b^2 = c^2 where a and b are legs and c is the hypotenuse.<BR>\n" );
document.write( "square the 18 to get 324<BR>\n" );
document.write( "your equation now becomes a^2 + b^2 = 324<BR>\n" );
document.write( "you can solve for a in terms of b or you can solve for b in terms of a but you can't solve for a or b directly because you have 1 equation with 2 unknowns.\r<BR>\n" );
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document.write( "if you assume a value for a, then you can find a value for b.<BR>\n" );
document.write( "if you assume a value for b, then  you can find a value for a.\r<BR>\n" );
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document.write( "let's assume that a is equal to 8.<BR>\n" );
document.write( "this means that a^2 = 64 and the equation becomes:<BR>\n" );
document.write( "64 + b^2 = 324<BR>\n" );
document.write( "subtract 64 from both sides of the equation to get b^2 = 324 - 64 which becomes b^2 = 260.<BR>\n" );
document.write( "take the square root of both sides of that equation to get b = sqrt(260).\r<BR>\n" );
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document.write( "you have a = 8 and b = sqrt(260).<BR>\n" );
document.write( "to find the hypotenuse use the pythagorean formula again to get:<BR>\n" );
document.write( "a^2 + b^2 = c^2 which becomes:<BR>\n" );
document.write( "8^ + sqrt(260)^2 = 18^2<BR>\n" );
document.write( "simplify to get 64 + 260 = 324<BR>\n" );
document.write( "combine like terms to get 324 = 324<BR>\n" );
document.write( "the equation is true so a = 8 and b = sqrt(260) is a solution to the equation.\r<BR>\n" );
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document.write( "to get this solution, you had to assume a = 8.<BR>\n" );
document.write( "if you are given the value of one of the legs and the hypotenuse, then you can solve for the other leg.\r<BR>\n" );
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