document.write( "Question 1210262: Let ABC be a triangle with side lengths AB = 5, BC = 6, and AC = 9. What is the area of the triangle with side lengths \tan A$, \tan B, and \tan C?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #851763 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Let ABC be a triangle with side lengths AB = 5, BC = 6, and AC = 9.
\n" ); document.write( "What is the area of the triangle with side lengths tan(A), tan(B), and tan(C)?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " This problem's formulation looks strange, but I will interpret it \" as is \",\r
\n" ); document.write( "\n" ); document.write( " i.e. in a way as I read it.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Compare  |AB|^2 + |BC|^2  with  |AC|^2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We have  5^2 + 6^2 = 25 + 36 = 61  for  |AB|^2 + |BC|^2  and  9^2 = 81  for  |AC|^2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since  |AB|^2 + |BC|^2 = 61  is  less  than  |AC|^2 = 81,  we conclude that  angle  B  is obtuse.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If so, then tan(B) is negative.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The implication is that such a triangle with the sides tan(A), tan(B) and tan(C) does not exist.\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" );