document.write( "Question 1205030: Given 30-60-90 triangle with sides p\sqrt(6) , p\sqrt(2 ), q\sqrt(3); find p, q
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #841640 by ikleyn(52873) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Given 30-60-90 triangle with sides p/sqrt(6) , p/sqrt(2 ), q/sqrt(3); find p, q
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Notice that I rewrote the condition using normal designations for the division operation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Two sides    and    have the ratio\r\n" );
document.write( "\r\n" );
document.write( "     =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In combination with the given fact that the triangle is 30-60-90, \r\n" );
document.write( "it means that    is  the shorter leg,  while    is  the longer leg.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    +-----------------------------------------------+\r\n" );
document.write( "    |      It admits only one interpretation,       |\r\n" );
document.write( "    |  and no other interpretation is admittable.   |\r\n" );
document.write( "    +-----------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence,  is the hypotenuse, and we can write\r\n" );
document.write( "\r\n" );
document.write( "     = \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(the hypotenuse length is twice the shorter leg), since the triangle is 30-60-90.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives  q =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the sides are:    is  the shorter leg,    is  the longer leg and   =   is the hypotenuse.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We can write then Pythagorean equation\r\n" );
document.write( "\r\n" );
document.write( "     +  = ,\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "     +  = ,\r\n" );
document.write( "\r\n" );
document.write( "     +  = ,\r\n" );
document.write( "\r\n" );
document.write( "     = ,\r\n" );
document.write( "\r\n" );
document.write( "     = ,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which is an identity.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At this point, the problem is solved in full.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  p can be any real positive number; then q = .  There are infinitely many solutions.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );