document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207377>Question 1207377</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the figure, a person standing at point A notices that the angle of elevation to the top of the antenna is 45° 30'. A second person standing 39.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be 44° 10'. How far is the person at A from the base of the antenna? (Round your answer to the nearest whole number.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845224 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> angle A is equal to 45 degrees 30 minutes = 45 + 30/60 = 45.5 degrees.<BR>\n" );
document.write( "angle B is equal to 44 degrees 10 minutes = 44 + 10/60 = 44.16666... degrees.\r<BR>\n" );
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document.write( "two triangle are formed with a common vertical side of h.<BR>\n" );
document.write( "the angle closest to h is angle A.<BR>\n" );
document.write( "the angle farthest to h is angle B.<BR>\n" );
document.write( "angle A has an adjacent side of x and an opposite side of h.<BR>\n" );
document.write( "angle B has an adjacent side of x + 39 and an opposite side of h.\r<BR>\n" );
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document.write( "you have tan(A) = h/x and you have tan(B) = h / (x + 39).\r<BR>\n" );
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document.write( "solve for h in both of those equations to get h = x * tan(A) and h = (x + 39) * tan(B).\r<BR>\n" );
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document.write( "simplify to get h = x * tan(A) and h = x * tan(B) + 39 * tan(B)\r<BR>\n" );
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document.write( "since h = h, then x * tan(A) = x * tan(B) + 39 * tan(B)\r<BR>\n" );
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document.write( "subtract x * tan(B) from both sides of the equation and factor out the x to get x * (tan(A) - tan(B)) = 39 * tan(B)\r<BR>\n" );
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document.write( "divide both sides of the equation by (tan(A) - tan(B)) to get x = 39 * tan(B) / (tan(A) - tan(B))\r<BR>\n" );
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document.write( "since A = 45.5 degrees and B = 44.166666..... degrees, you get x = 39 * tan(44.166666...) / (tan(45.5 - tan(44.166666...) = 818.5122291.\r<BR>\n" );
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document.write( "that's how far point A is from the base of the antenna.\r<BR>\n" );
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document.write( "i confirmed the value of x was correct, because:\r<BR>\n" );
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document.write( "h = tan(A) * x = tan(45.5) * 818.5122291 = 832.9240955 and .....<BR>\n" );
document.write( "h = tan(B) * (x + 39) = tan(44.16666...) * 857.5122291 = 832.9240955.<BR>\n" );
document.write( "they're the same value as they should be.\r<BR>\n" );
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document.write( "here's my diagram.\r<BR>\n" );
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document.write( "i used storage of ti-84 plus to hold the values.<BR>\n" );
document.write( "those storage locations are A, B, C, D, E, and F indicated by ----> .....\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo<BR>\n" );
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