document.write( "Question 560304: From a certain point you observe that the top of a cliff has an angle of elevation of 45deg. If you move 60 metres directly away from the cliff along the horizontal ground, the angle of elevation is now observed to be 30deg. how high is the cliff?
\n" ); document.write( "Help please \n" ); document.write( "

Algebra.Com's Answer #363817 by mananth(16946) $\"\"$ $\"About$

You can put this solution on YOUR website!
first observation\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "45 deg
\n" ); document.write( "let distance from clif be x
\n" ); document.write( "Tan $\"theta\"$ = opposite side / afjacent side\r
\n" ); document.write( "\n" ); document.write( "tan 45 = h/x
\n" ); document.write( "x tan 45 = h\r
\n" ); document.write( "\n" ); document.write( "similarly\r
\n" ); document.write( "\n" ); document.write( "(x+60)*tan 30 =h\r
\n" ); document.write( "\n" ); document.write( "tan30*(x+60)=x * tan 45\r
\n" ); document.write( "\n" ); document.write( "x tan 30+ 60 tan 60 = x *tan 45\r
\n" ); document.write( "\n" ); document.write( "x tan 30 -xtan 45 = -60 * tan 60\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "x(tan 30-Tan 45)=-60*tan 30
\n" ); document.write( "x=-60*tan 30/(tan 30-Tan 45)
\n" ); document.write( "x=-34.64/-0.422
\n" ); document.write( "x=82 \r
\n" ); document.write( "\n" ); document.write( "tan 45 = h/82
\n" ); document.write( "82*tan 45 = h\r
\n" ); document.write( "\n" ); document.write( "height of cliff = 82m\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );