document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151609>Question 1151609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a pilot flying horizontally at a constant height, measures the angle of depression to a landmark to be 18 degrees. After flying 700m, the new angle of depression to the landmark is 21 degrees. At what height is the pilot flying. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773445 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=773445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are at least two methods to solve this problem.\r<BR>\n" );
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document.write( "Method 1\r<BR>\n" );
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document.write( "Construct the diagram to look something like this. The goal is to find h<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/Dx1z8rN.png\"><BR>\n" );
document.write( "The diagram is not to scale.<BR>\n" );
document.write( "Point A = plane's starting position<BR>\n" );
document.write( "Point B = plane's position after flying 700 meters<BR>\n" );
document.write( "Point C = landmark on the ground<BR>\n" );
document.write( "Point D = used to help form the angle of depression of 21 degrees<BR>\n" );
document.write( "Point E = point on ground directly under point A<BR>\n" );
document.write( "Point F = point on ground directly under point B<BR>\n" );
document.write( "Each pair of adjacent red and blue angles add up to 90 degrees (ie they are complementary angles)\r<BR>\n" );
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document.write( "The diagram may seem a bit cluttered, so you can peel triangle AEC and triangle BFC apart to get this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/68ebrmJ.png\"><BR>\n" );
document.write( "Focus on triangle BFC<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(B) = FC/FB<BR>\n" );
document.write( "tan(69) = x/h<BR>\n" );
document.write( "h*tan(69) = x<BR>\n" );
document.write( "x = h*tan(69)\r<BR>\n" );
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document.write( "Move onto triangle AEC<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(A) = EC/AE<BR>\n" );
document.write( "tan(72) = (700+x)/h<BR>\n" );
document.write( "tan(72) = (700+h*tan(69))/h ... plug in x = h*tan(69)<BR>\n" );
document.write( "h*tan(72) = 700+h*tan(69)<BR>\n" );
document.write( "h*tan(72)-h*tan(69) = 700<BR>\n" );
document.write( "h*(tan(72)-tan(69)) = 700<BR>\n" );
document.write( "h = 700/(tan(72)-tan(69))<BR>\n" );
document.write( "<font color=red size=4>h = 1481.18533068004 is the approximate height in meters.</font>\r<BR>\n" );
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document.write( "Method 2\r<BR>\n" );
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document.write( "The diagram will be similar, but it now looks like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/X7hNM9j.png\"><BR>\n" );
document.write( "The diagram is not to scale.<BR>\n" );
document.write( "Points A,B,C,D are defined the same way as in the previous diagram.<BR>\n" );
document.write( "Angle B = 159 because angle ABC = 180-(angle DBC) = 180-21 = 159<BR>\n" );
document.write( "Angle C = 3 degrees comes from the fact that A+B+C = 180\r<BR>\n" );
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document.write( "Focus solely on triangle ABC (ie ignore point D)<BR>\n" );
document.write( "Use the law of sines to find side 'a'.<BR>\n" );
document.write( "a/sin(A) = c/sin(C)<BR>\n" );
document.write( "a/sin(18) = 700/sin(3)<BR>\n" );
document.write( "a = sin(18)*700/sin(3)<BR>\n" );
document.write( "a = 4133.14118229429\r<BR>\n" );
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document.write( "Now we can use the SAS triangle area formula<BR>\n" );
document.write( "area = (1/2)*side1*side2*sin(included angle)<BR>\n" );
document.write( "area = (1/2)*a*c*sin(B)<BR>\n" );
document.write( "area = (1/2)*4133.14118229429*700*sin(159)<BR>\n" );
document.write( "area = 518414.865738014<BR>\n" );
document.write( "This is the approximate area of triangle ABC.\r<BR>\n" );
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document.write( "Finally, turn to the formula<BR>\n" );
document.write( "area = (1/2)*base*height<BR>\n" );
document.write( "to help find the height of the triangle ABC\r<BR>\n" );
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document.write( "area = (1/2)*base*height<BR>\n" );
document.write( "518414.865738014 = (1/2)*700*h<BR>\n" );
document.write( "518414.865738014*2 = 700*h<BR>\n" );
document.write( "1036829.73147602 = 700*h<BR>\n" );
document.write( "700*h = 1036829.73147602<BR>\n" );
document.write( "h = 1036829.73147602/700<BR>\n" );
document.write( "<font color=red size=4>h = 1481.18533068002 which was roughly the same approximate height we got earlier.</font><BR>\n" );
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