document.write( "Question 1195197: The angle of elevation of the top of a mast from a point A is 30°. When the observer moves 20 metres towards the foot of the mast, the angle of elevation becomes 45°.Calculate, to the nearest metre, the height of the mast. \n" ); document.write( "

Algebra.Com's Answer #827617 by ikleyn(52782) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The angle of elevation of the top of a mast from a point A is 30°.
\n" ); document.write( "When the observer moves 20 metres towards the foot of the mast,
\n" ); document.write( "the angle of elevation becomes 45°.
\n" ); document.write( "Calculate, to the nearest metre, the height of the mast.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Make a sketch.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let x be the height of the mast, in meters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the sketch, find two righ-angled triangles with the right angle\r\n" );
document.write( "at the base of the mast.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The distance of the point A from the mast is  .\r\n" );
document.write( "\r\n" );
document.write( "The distance of the other point from the mast is  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The difference of these distances is 20 meters, as it is given in the problem, \r\n" );
document.write( "so you can write this equation\r\n" );
document.write( "\r\n" );
document.write( "     -  = 20,\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "    x = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, tan(30°) =  = 0.57735  and tan(45°) = 1,  so\r\n" );
document.write( "\r\n" );
document.write( "    x =  = use your calculator = 27 meters (rounded to the nearest meter).    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "=================\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Comment from student : please show me the sketch\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "My response : I won't even think about doing a sketch for you.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

Making sketches is the students' honorable duty and a privilege (!)

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Making sketches for a student is not a tutors' job.     <<<---===     it would be ANTI-pedagogic from my side to do it . . . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "//////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hey, what I said above, is the $\"highlight%28highlight%28highlight%28CREDO%29%29%29\"$ of a fair student.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "************************************************************************\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        Please confirm by posting a message to me, that you do understand \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "                my writing and agree with this CREDO of a fair student.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "************************************************************************\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );