document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=552117>Question 552117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypoteneuse of a right triangle is 19 inches.  How can I calculate the lengths of the base and height?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360130 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=360130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> hypotenuse is 19 inches.<BR>\n" );
document.write( "length and width cannot be calculated exactly from this information.<BR>\n" );
document.write( "the formula for the hypotenuse of a right triangle is:<BR>\n" );
document.write( "c^2 = a^2 + b^2 where:<BR>\n" );
document.write( "c is the hypotenuse<BR>\n" );
document.write( "a is one leg<BR>\n" );
document.write( "b is the other leg.<BR>\n" );
document.write( "you can find what a^2 and b^2 are equal to.<BR>\n" );
document.write( "the formula becomes:<BR>\n" );
document.write( "19^2 = a^2 + b^2 which becomes:<BR>\n" );
document.write( "361 = a^2 + b^2<BR>\n" );
document.write( "this doesn't tell you how long \"a\" is or how long \"b\" is.<BR>\n" );
document.write( "if you assume a value for \"a\", then you can calculate a value for \"b\" and vice versa.<BR>\n" );
document.write( "the value of \"a\" can be any length smaller than 19.<BR>\n" );
document.write( "assume \"a\" is 18, then \"b\" can be calculated as:<BR>\n" );
document.write( "a^2 + b^2 = c^2 becomes:<BR>\n" );
document.write( "18^2 + b^2 = 19^2 which becomes:<BR>\n" );
document.write( "324 + b^2 = 361<BR>\n" );
document.write( "subtract 324 from both sides of this equation to get:<BR>\n" );
document.write( "b^2 = 361 - 324<BR>\n" );
document.write( "take the square root of both sides of this equation to get:<BR>\n" );
document.write( "b = sqrt(37)<BR>\n" );
document.write( "this results in:<BR>\n" );
document.write( "b = 6.08276253<BR>\n" );
document.write( "assume another value for \"a\" and you'll get a different value for \"b\".<BR>\n" );
document.write( "in order to nail down a value for the legs of the triangle, you would need:<BR>\n" );
document.write( "the value of a, or:<BR>\n" );
document.write( "the value of b, or:<BR>\n" );
document.write( "one of the angles of the triangle other than the 90 degree angle.<BR>\n" );
document.write( "just knowing the value of c (the hypotenuse) is not enough.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );