document.write( "Question 1210261: Acute triangle ABC has \sin A = \dfrac{2}{5} and \sin B = \dfrac{2}{\sqrt{7}}. What is \sin C? \n" ); document.write( "

Algebra.Com's Answer #851761 by ikleyn(52810) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Acute triangle ABC has sin(A) = $\"2%2F5\"$ and sin(B) = $\"2%2Fsqrt%287%29\"$ . What is sin(C) ?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Since sin(A) =   and angle A is acute (given), we have\r\n" );
document.write( "\r\n" );
document.write( "    A =  = 23.5781785 degrees.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since sin(B) =   and angle B is acute (given), we have\r\n" );
document.write( "\r\n" );
document.write( "    B =  = arcsin(0.755928946) = 49.1066053 degrees.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore,  C = 180 - 23.5781785 - 49.1066053 = 107.3152162 degrees.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then  sin(C) = 0.95468179116.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  sin(C)  is about  0.95468179116.\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( "----------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

A post-solution note

\r
\n" ); document.write( "\n" ); document.write( "        As I solved the problem to the end, I see that its formulation \r
\n" ); document.write( "\n" ); document.write( "        is FATALLY INCORRECT and is SELF-CONTRADICTORY.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        Indeed, the problem says that the given triangle is acute, \r
\n" ); document.write( "\n" ); document.write( "        which means that all three its angles are acute.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        But the angle C, as I found it, is OBTUSE:   its measure is about 107 degrees.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

So, this problem simply DECEIVES a reader,
\n" ); document.write( "which is $\"highlight%28highlight%28unacceptable%29%29\"$ for a Math problem.

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

\n" );

A post-solution note

So, this problem simply DECEIVES a reader,\n" ); document.write( "which is for a Math problem.

So, this problem simply DECEIVES a reader,
\n" ); document.write( "which is $\"highlight%28highlight%28unacceptable%29%29\"$ for a Math problem.