document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196263>Question 1196263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At point \"A\" due east to a hut, the angle of elevation is 55° and at point \"B\" due it's west the angle of elevation is 45°. The distance from point A to B is 15m. Find height of the hut?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829021 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=829021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "This is one way to draw out the diagram<BR>\n" );
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document.write( "Let x be the length of segment AD<BR>\n" );
document.write( "And let y be the height of the hut (i.e. the length of segment CD)\r<BR>\n" );
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document.write( "Triangle BCD is a 45-45-90 triangle<BR>\n" );
document.write( "The two legs (BD and CD) are the same length<BR>\n" );
document.write( "So BD = y and CD = y\r<BR>\n" );
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document.write( "AB = 15<BR>\n" );
document.write( "AD = x<BR>\n" );
document.write( "BD = AB - AD<BR>\n" );
document.write( "BD = 15 - x\r<BR>\n" );
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document.write( "Since BD = y was mentioned earlier, and BD = 15-x, we can say y = 15-x\r<BR>\n" );
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document.write( "For triangle ACD, we can say:<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(A) = CD/AD<BR>\n" );
document.write( "tan(55) = y/x<BR>\n" );
document.write( "x*tan(55) = y<BR>\n" );
document.write( "y = x*tan(55)\r<BR>\n" );
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document.write( "Now plug in y = 15-x and solve for x<BR>\n" );
document.write( "y = x*tan(55)<BR>\n" );
document.write( "15-x = x*tan(55)<BR>\n" );
document.write( "15 = x*tan(55)+x<BR>\n" );
document.write( "x*tan(55)+x = 15<BR>\n" );
document.write( "x*(tan(55)+1) = 15<BR>\n" );
document.write( "x = 15/(tan(55)+1)<BR>\n" );
document.write( "x = 6.17754764468651\r<BR>\n" );
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document.write( "Then use this to find the value of y<BR>\n" );
document.write( "y = 15-x<BR>\n" );
document.write( "y = 15-6.17754764468651<BR>\n" );
document.write( "y = 8.8224523553135<BR>\n" );
document.write( "y = 8.822452<BR>\n" );
document.write( "Or,<BR>\n" );
document.write( "y = x*tan(55)<BR>\n" );
document.write( "y = 6.17754764468651*tan(55)<BR>\n" );
document.write( "y = 8.82245235531349<BR>\n" );
document.write( "y = 8.822452\r<BR>\n" );
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document.write( "Answer: Approximately 8.822452 meters\r<BR>\n" );
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document.write( "Similar question:<BR>\n" );
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