document.write( "Question 165933: I need help with a question could someone please help??\r
\n" ); document.write( "\n" ); document.write( "Find the length, to the nearest tenth, of the apothem of a regular octogon whose sides are each 10 inches long? \n" ); document.write( "

Algebra.Com's Answer #122321 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
Edwin's solution:
\n" ); document.write( "Warning: MRperkins's solution is correct up to the last step.
\n" ); document.write( "He apparently mis-pressed something on his calculator and got
\n" ); document.write( "the wrong answer. Here is my complete solution with drawings:\r
\n" ); document.write( "\n" ); document.write( "I need help with a question could someone please help??
\n" ); document.write( "
\n" ); document.write( "Find the length, to the nearest tenth, of the apothem of a regular octogon whose sides are each 10 inches long?
\n" ); document.write( "

  \r\n" );
document.write( "Draw the octagon, all sides of which are 10 inches.\r\n" );
document.write( "I'll just indicate that the bottom side is 10:\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Now temporarily, connect the vertices\r\n" );
document.write( "to the center:\r\n" );
document.write( "\r\n" );
document.write( "I did that just to show that each\r\n" );
document.write( "of those 8 angles at the center are\r\n" );
document.write( "° = °, so that if we\r\n" );
document.write( "erase all but the bottom two, like this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we know that the angle in the\r\n" );
document.write( "above is °\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now draw in an apothem, the line from\r\n" );
document.write( "the center to the midpoint of the bottom\r\n" );
document.write( " side, and label it .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since the sides\r\n" );
document.write( "of the octagon are 10 each, the two parts of\r\n" );
document.write( "the bottom side are 5 each. Also the 45° angle\r\n" );
document.write( "is bisected into two angles which are 22.5° each\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So lets take away everything but\r\n" );
document.write( "just this little right triangle:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then we just do a little trig on that triangle:\r\n" );
document.write( "\r\n" );
document.write( "The side opposite the 22.5° angle is 5 and the\r\n" );
document.write( "side adjacent to it is a, so\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by a:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by tan(22.5°):\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "or, to the nearest tenth,\r\n" );
document.write( "\r\n" );
document.write( " inches.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );