document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999146>Question 999146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a hiker approximates an angle at the top of a hill to be 22 degrees. After walking 700 feet closer, the hiker estimates to angle of elevation increased by 16 degrees. How high is the hill? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616838 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=616838\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The height of the hill is x feet above the hiker.<BR>\n" );
document.write( "The tangent of the height is x/the distance the hiker is from the perpendicular.  <BR>\n" );
document.write( "tan 22=0.4040=x/distance(d)<BR>\n" );
document.write( "700 feet closer, the angle is now 38 degrees.<BR>\n" );
document.write( "The height hasn't changed, but the distance is less<BR>\n" );
document.write( "tan 38=0.7813=x/(d-700)<BR>\n" );
document.write( "0.7813*(d-700)=0.4040d , because both of these tangents are equal to the same x or height, so they are equal to each other.<BR>\n" );
document.write( "0.7813d-546.90=0.404d<BR>\n" );
document.write( "0.3773d=546.90<BR>\n" );
document.write( "d=1449.51 ft.  THAT IS NOT THE HEIGHT, ONLY THE LENGTH OF THE ADJACENT SIDE.<BR>\n" );
document.write( "TAN 22=X/1449.51<BR>\n" );
document.write( "1449.51*0.404=585.60 FEET<BR>\n" );
document.write( "check with the other<BR>\n" );
document.write( "749.51*0.7813=585.58 FEET, the same given rounding error. </SPAN>\n" );
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