document.write( "Question 1014220: There are two towers. One at A and one at B. A and B are are two points on the same horizontal ground and 120 m apart. The angle of elevation of the top of the tower at B as observed from A is twice that of the tower at A as observed at B. At C, midway between A and B, the angles of elevation are complimentary. Find the heights of the the towers.\r
\n" ); document.write( "\n" ); document.write( "I really need the answers ASAP. I'm going to pass this take home quiz tomorrow at 8:30 AM, Philippine time (GMT +8). I suck at math, so I don't know what to do. Thank you so so so much :) \n" ); document.write( "

Algebra.Com's Answer #630622 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "There are two towers. One at A and one at B. A and B are are two points on the same horizontal ground and 120 m apart.
\n" ); document.write( "The angle of elevation of the top of the tower at B as observed from A is twice that of the tower at A as observed at B.
\n" ); document.write( "At C, midway between A and B, the angles of elevation are complimentary. Find the heights of the the towers.\r
\n" ); document.write( "\n" ); document.write( "I really need the answers ASAP. I'm going to pass this take home quiz tomorrow at 8:30 AM, Philippine time (GMT +8).
\n" ); document.write( "I suck at math, so I don't know what to do. Thank you so so so much :)
\n" ); document.write( "---------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer. The lower tower is 40 m height. The higher tower is 90 m height.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solution\r
\n" ); document.write( "\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( "The scheme is shown in the Figure to the right.\r\n" );
document.write( "The vertical lines AE and BF represent the towers.\r\n" );
document.write( "The angle ECF formed by green lines is the right angle.                        \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Due to this reason, the triangles ACE and BFC are similar \r\n" );
document.write( "  (and their respective vertices are listed in an corresponding order).\r\n" );
document.write( "\r\n" );
document.write( "From the triangles similarity, we have a proportion  = , or \r\n" );
document.write( " = .   (1)\r\n" );
document.write( "\r\n" );
document.write( "In addition to it, from the condition we have these equalities:\r\n" );
document.write( "\r\n" );
document.write( "h =   and  H =  = .      (2)\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Substituting (2) into (1) we get this equation:   = . \r\n" );
document.write( "\r\n" );
document.write( "After canceling by 60, you will get  = ,  or   = .   (3)\r\n" );
document.write( "\r\n" );
document.write( "Replacing here  = ,  you will get the equation\r\n" );
document.write( "\r\n" );
document.write( " = .  (4)\r\n" );
document.write( "\r\n" );
document.write( "To solve it, introduce new variable x = .  You will get \r\n" );
document.write( "\r\n" );
document.write( "4x =   --->   =   --->   =   --->  x = .\r\n" );
document.write( "\r\n" );
document.write( "Thus   = ,  and you just have   h =  =  = 40 m.\r\n" );
document.write( "\r\n" );
document.write( "Next,  =  = . . . = ,  and you finally get \r\n" );
document.write( "\r\n" );
document.write( "H =  =  = 90 m.\r\n" );
document.write( "

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

\n" );