document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154926>Question 1154926</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thank you for the help:\r<BR>\n" );
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document.write( "You are in a plane flying at an altitude of 900 feet. You see a statue at an angle of depression at 57 degrees.  You also see a building at an angle of depression at 68 degrees.  How far is the statue from the building? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777427 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=777427\">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 one way to draw the diagram. The diagram is not to scale.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"50%\" src = \"https://i.imgur.com/bF1Vwne.png\"><BR>\n" );
document.write( "The points are defined as follows:<BR>\n" );
document.write( "A = base of the statue<BR>\n" );
document.write( "B = base of the building<BR>\n" );
document.write( "C = point on the ground directly under point D<BR>\n" );
document.write( "D = plane's location<BR>\n" );
document.write( "E = point to help label the angles of depression\r<BR>\n" );
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document.write( "The lengths we'll work with are<BR>\n" );
document.write( "CD = 900 (height)<BR>\n" );
document.write( "AB = x  (distance between statue and building)<BR>\n" );
document.write( "BC = y\r<BR>\n" );
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document.write( "The given angles of depression are<BR>\n" );
document.write( "angle ADE = 57 degrees (the upper angle shown in red)<BR>\n" );
document.write( "angle BDE = 68 degrees (the upper angle shown in blue)\r<BR>\n" );
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document.write( "Because DE and AC are horizontal lines, they are parallel. So we know that the alternate interior angles are congruent. This makes,<BR>\n" );
document.write( "angle DAC = 57 degrees (the lower angle shown in red)<BR>\n" );
document.write( "angle DBC = 68 degrees (the lower angle shown in blue)\r<BR>\n" );
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document.write( "In other words,<BR>\n" );
document.write( "angle ADE = angle DAC = 57 (red pair of angles)<BR>\n" );
document.write( "angle BDE = angle DBC = 68 (blue pair of angles)<BR>\n" );
document.write( "because they are alternate interior angle pairs.\r<BR>\n" );
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document.write( "For now, focus your attention on right triangle BCD.<BR>\n" );
document.write( "Ignore points A and E. Ignore the 57 degree angle for now.<BR>\n" );
document.write( "When we focus solely on triangle BCD, the label \"angle DBC\" can be simplified to the label \"angle B\". So B = 68.\r<BR>\n" );
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document.write( "We'll use the tangent ratio to solve for y.<BR>\n" );
document.write( "Recall the tangent of an angle is the ratio of the opposite over adjacent.\r<BR>\n" );
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document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(B) = CD/BC .... again we're only focusing on triangle BCD<BR>\n" );
document.write( "tan(68) = 900/y<BR>\n" );
document.write( "y*tan(68) = 900<BR>\n" );
document.write( "y = 900/tan(68)<BR>\n" );
document.write( "y = 363.623603251641 ... use a calculator here; value is approximate<BR>\n" );
document.write( "Make sure your calculator is in degree mode.\r<BR>\n" );
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document.write( "Now we can use this to find x. We'll use another tangent ratio. This time, focus on triangle ACD. Ignore point B and its associated angle. Ignore point E.\r<BR>\n" );
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document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(A) = CD/AC<BR>\n" );
document.write( "tan(A) = CD/(AB+BC)<BR>\n" );
document.write( "tan(57) = 900/(x+y)<BR>\n" );
document.write( "tan(57) = 900/(x+363.623603251641)\r<BR>\n" );
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document.write( "Do a bit of algebra to solve for x. It might help to replace \"tan(57)\" with a variable such as z. \r<BR>\n" );
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document.write( "tan(57) = 900/(x+363.623603251641)<BR>\n" );
document.write( "z = 900/(x+363.623603251641)<BR>\n" );
document.write( "z(x+363.623603251641) = 900<BR>\n" );
document.write( "zx+363.623603251641z = 900<BR>\n" );
document.write( "zx = 900-363.623603251641z<BR>\n" );
document.write( "x = (900-363.623603251641z)/z<BR>\n" );
document.write( "x = (900-363.623603251641*tan(57))/(tan(57)) ... plug in z = tan(57)<BR>\n" );
document.write( "x = 220.843230626119<BR>\n" );
document.write( "I used a calculator for the last step. This value is approximate as well.\r<BR>\n" );
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document.write( "No rounding instructions were given, so I would ask what your teacher wants you to round to. For now I'll just round to the nearest whole number.\r<BR>\n" );
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document.write( "Answer:  <font color=red size=4>Approximately 221 feet</font>\r<BR>\n" );
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document.write( "Edit: the tutor @MathTherapy has a much more elegant solution, so I would go with that method instead. Though the diagram is still handy to have. \r<BR>\n" );
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