document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145693>Question 1145693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a person standing at point A notices that the angle of elevation to the top of the antenna is 48° 30'. A second person standing 35.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be 41° 10'. How far is the person at A from the base of the antenna? \r<BR>\n" );
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document.write( "(Round your answer to the nearest whole number.)<BR>\n" );
document.write( "________ft  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #766982 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=766982\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  a person standing at point A notices that the angle of elevation to the top of the antenna is 48° 30'.<BR>\n" );
document.write( " A second person standing 35.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be 41° 10'.<BR>\n" );
document.write( " How far is the person at A from the base of the antenna?<BR>\n" );
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document.write( "let x = the distance from A to the base of the antenna<BR>\n" );
document.write( "let h = the vertical height of the antenna<BR>\n" );
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document.write( "Change 48 30' to 48.5 degrees, change 41 10' to 41.167 degrees<BR>\n" );
document.write( "Use the tangent of these two angles<BR>\n" );
document.write( "tan(48.5) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Fx ALIGN=MIDDLE  ALT=\"h%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "tan(48.5)x = h<BR>\n" );
document.write( "and<BR>\n" );
document.write( "tan(41.167) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F%28%28x%2B35%29%29 ALIGN=MIDDLE  ALT=\"h%2F%28%28x%2B35%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "tan(41.167)(x+35) = h<BR>\n" );
document.write( "h = h therefore<BR>\n" );
document.write( "tan(48.5)x = tan(41.167)(x+35)<BR>\n" );
document.write( "find the actual tangent of these two angles<BR>\n" );
document.write( "1.1303x = .8744(x+35)<BR>\n" );
document.write( "1.1303x = .8744x + 30.6<BR>\n" );
document.write( "1.1303x - .8744x = 30.6<BR>\n" );
document.write( ".2559x = 30.6<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30.6%2F.2559 ALIGN=MIDDLE  ALT=\"30.6%2F.2559\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 119.58, 120 ft from A to the base of the Antenna<BR>\n" );
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document.write( "you can confirm this, find the height of the antenna using both positions<BR>\n" );
document.write( "tan(48.5)*120 = 135.6 ft<BR>\n" );
document.write( "tan(41.167)*155 = 135.5 ft, close enough </SPAN>\n" );
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