document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058385>Question 1058385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> from the top of a cliff the angles of depression of two boats in the same vertical plane at the observer's eyes are 30 E and 45. if the distance between the boats is 100 feet, find the height of the cliff </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673438 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=673438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw this and the angle from the boat to the cliff is 30 degrees.<BR>\n" );
document.write( "The other boat has an angle of 45 degrees.<BR>\n" );
document.write( "The cliff height is x<BR>\n" );
document.write( "the distance to the first boat is y, to the second boat y+100<BR>\n" );
document.write( "tangent 30=x/(y+100)<BR>\n" );
document.write( "tangent 45=x/y<BR>\n" );
document.write( "Therefore, y=x, since tan 45=1<BR>\n" );
document.write( "sqrt(3)/3=x/(x+100) substituting and knowing tan 30 is sqrt (3)/3<BR>\n" );
document.write( "0.5774(x+100)=x<BR>\n" );
document.write( "0.5774x+57.74=x<BR>\n" );
document.write( "57.74=0.4226 x<BR>\n" );
document.write( "dividing out<BR>\n" );
document.write( "136.63 or 136 feet.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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