document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198040>Question 1198040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From a point A on level ground, the angle of elevation to the top of a tree is 38 degrees. <BR>\n" );
document.write( "From point B that is 46 feet farther from the tree, the angle of elevation is 22 degrees. What is the height of the tree?\r<BR>\n" );
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document.write( "One of the possible answers are below:<BR>\n" );
document.write( "A) 34.1 feet <BR>\n" );
document.write( "B) 35.8 feet <BR>\n" );
document.write( "C) 36.7 feet <BR>\n" );
document.write( "D) 37.2 feet <BR>\n" );
document.write( "E) 38.5 feet  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831552 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=831552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Here's a slight alternative approach to what the tutor Edwin McCravy has written. <BR>\n" );
document.write( "I'll be using his diagram and the notation he set up of u = tan(38), v = tan(22)\r<BR>\n" );
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document.write( "The slight different approach is to let<BR>\n" );
document.write( "BG = x<BR>\n" );
document.write( "BA = 46<BR>\n" );
document.write( "AG = x-46\r<BR>\n" );
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document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(angle TBG) = TG/BG<BR>\n" );
document.write( "tan(22) = y/x<BR>\n" );
document.write( "y = x*tan(22)\r<BR>\n" );
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document.write( "tan(38) = y/(x-46)<BR>\n" );
document.write( "tan(38) = x*tan(22)/(x-46) .... plug in y = x*tan(22)<BR>\n" );
document.write( "u = x*v/(x-46) .... make replacements for u and v<BR>\n" );
document.write( "u(x-46) = xv<BR>\n" );
document.write( "ux - 46u = xv<BR>\n" );
document.write( "ux-xv = 46u<BR>\n" );
document.write( "x(u-v) = 46u<BR>\n" );
document.write( "x = 46u/(u-v)<BR>\n" );
document.write( "x = 46*tan(38)/(tan(38)-tan(22))<BR>\n" );
document.write( "x = 95.263733005284, which is the approximate length of segment BG.\r<BR>\n" );
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document.write( "y = x*tan(22)<BR>\n" );
document.write( "y = 95.263733005284*tan(22)<BR>\n" );
document.write( "y = 38.489046505093<BR>\n" );
document.write( "y = 38.5, which is the approximate length of segment TG.\r<BR>\n" );
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document.write( "Answer: <font color=red>E) 38.5 feet</font>\r<BR>\n" );
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document.write( "Yet another approach\r<BR>\n" );
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document.write( "Refer to the diagram Edwin McCravy has drawn.\r<BR>\n" );
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document.write( "Angle TAG = 38 degrees.<BR>\n" );
document.write( "angle TAB = 180-angle TAG = 180-38 = 142 degrees<BR>\n" );
document.write( "This is angle A of triangle TAB.\r<BR>\n" );
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document.write( "Focus on triangle TAB<BR>\n" );
document.write( "The interior angles T, A, B must add to 180 degrees.<BR>\n" );
document.write( "T + A + B = 180<BR>\n" );
document.write( "T + 142 + 22 = 180<BR>\n" );
document.write( "T + 164 = 180<BR>\n" );
document.write( "T = 180 - 164<BR>\n" );
document.write( "T = 16\r<BR>\n" );
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document.write( "Use the law of sines to find side 'a' which is opposite angle A.\r<BR>\n" );
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document.write( "sin(A)/a = sin(T)/t<BR>\n" );
document.write( "sin(142)/a = sin(16)/46<BR>\n" );
document.write( "46*sin(142) = a*sin(16)<BR>\n" );
document.write( "a = 46*sin(142)/sin(16)<BR>\n" );
document.write( "a = 102.74524576336<BR>\n" );
document.write( "This is the approximate length of segment TB.\r<BR>\n" );
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document.write( "Then focus on triangle TBG to say the following:<BR>\n" );
document.write( "sin(angle) = opposite/hypotenuse<BR>\n" );
document.write( "sin(angle TBG) = TG/TB<BR>\n" );
document.write( "sin(22) = y/102.74524576336<BR>\n" );
document.write( "y = 102.74524576336*sin(22)<BR>\n" );
document.write( "y = 38.489046505093<BR>\n" );
document.write( "y = 38.5\r<BR>\n" );
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document.write( "Answer: <font color=red>E) 38.5 feet</font><BR>\n" );
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