document.write( "Question 1026992: Prove that in any triangle that has the sides proportionate with 4, 5 and 6, the least angle measure is half of the biggest angle measure.
\n" ); document.write( "With the Cosinus Theorem, I found that(AB=4k , AC=5k, BC=6k)
\n" ); document.write( "cos A = 2/16
\n" ); document.write( "cos B = 9/16
\n" ); document.write( "cos C = 12/16
\n" ); document.write( "Help me, I dont know what to do further! \n" ); document.write( "

Algebra.Com's Answer #642266 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Prove that in any triangle that has the sides proportionate with 4, 5 and 6, the least angle measure is half of the biggest angle measure.
\n" ); document.write( "With the Cosinus Theorem, I found that(AB=4k , AC=5k, BC=6k)
\n" ); document.write( "cos A = 2/16
\n" ); document.write( "cos B = 9/16
\n" ); document.write( "cos C = 12/16
\n" ); document.write( "Help me, I dont know what to do further!
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "1.  I checked your calculations for cosines and confirm that they are correct.\r\n" );
document.write( "\r\n" );
document.write( "2. Now calculate .   (Notice that in your notations A is the largest angle, since it is opposite to the longest side BC.)\r\n" );
document.write( "\r\n" );
document.write( "   Use the formula for the cosines of the half argument of Trigonometry   \r\n" );
document.write( "\r\n" );
document.write( "    = .         (See the lesson Trigonometric functions of half argument in this site).\r\n" );
document.write( "\r\n" );
document.write( "   You will get   =  =  =  =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "3.  Hence, the angle    is congruent to the angle  C.   (They both are acute.)\r\n" );
document.write( "\r\n" );
document.write( "4.  Proved.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "I didn't know this fact before. It is new for me. Thanks !\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );