document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828543>Question 828543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It is a common experience to hear the sound of a low flying airplane, and look at the wrong place in the sky to see the plane. Suppose that a plane is traveling directly toward you at a speed of 200 mph and an altitude of 3,000 feet, and you hear the sound at what seems to be an angle of inclination of 20 degrees.<BR>\n" );
document.write( "At what angle should you actually look in order to see the plane? Assume the speed of sound is 1,100 ft/sec\r<BR>\n" );
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document.write( "Thank you in advance for you help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499527 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=499527\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is a common experience to hear the sound of a low flying airplane, and look at the wrong place in the sky to see the plane.<BR>\n" );
document.write( " Suppose that a plane is traveling directly toward you at a speed of 200 mph and an altitude of 3,000 feet, and you hear the sound at what seems to be an angle of inclination of 20 degrees.<BR>\n" );
document.write( "At what angle should you actually look in order to see the plane?<BR>\n" );
document.write( " Assume the speed of sound is 1,100 ft/sec<BR>\n" );
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document.write( "Draw a diagram showing the two right triangles formed by this problem<BR>\n" );
document.write( "One where sound originate from and one where the plane is now<BR>\n" );
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document.write( "since we will be dealing in seconds, find the speed of the aircraft in ft/sec<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28200%2A5280%29%2F3600 ALIGN=MIDDLE  ALT=\"%28200%2A5280%29%2F3600\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 293.3 ft/sec<BR>\n" );
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document.write( "Find the slant range to the point where the sound originated<BR>\n" );
document.write( "That will be the hypotenuse of a right triangle formed with ground and<BR>\n" );
document.write( "the height of the aircraft (3000')<BR>\n" );
document.write( "sin(20) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000%2Fh%29%29%29%0D%0Ah+=+%7B%7B%7B3000%2Fsin%2820%29 ALIGN=MIDDLE  ALT=\"3000%2Fh%29%29%29%0D%0Ah+=+%7B%7B%7B3000%2Fsin%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 8771.4 ft<BR>\n" );
document.write( "Find how long it will take the sound to travel this distance at 1100 ft/s<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8771.4%2F1100 ALIGN=MIDDLE  ALT=\"8771.4%2F1100\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7.974 sec <BR>\n" );
document.write( "Find how far the aircraft will travel in 7.974 sec<BR>\n" );
document.write( "7.874 * 293.3 = 2338.8 ft towards you<BR>\n" );
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document.write( "Now we are dealing with a new right triangle, find the distance from you to<BR>\n" );
document.write( "a point below where the aircraft is now<BR>\n" );
document.write( "Using the original triangle find the distance below the original point<BR>\n" );
document.write( "cos(20) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F8771.4 ALIGN=MIDDLE  ALT=\"d%2F8771.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = 8771.4 * cos(20)<BR>\n" );
document.write( "d = 8242.4 ft<BR>\n" );
document.write( "Find the distance to the point below the aircraft now<BR>\n" );
document.write( "8242.4 - 2338.8 = 5903.6, (subtracted the distance the aircraft traveled)<BR>\n" );
document.write( "Find the new angle (A) using the above and 3000ft<BR>\n" );
document.write( "ArcTan(A) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000%2F5903.6 ALIGN=MIDDLE  ALT=\"3000%2F5903.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A = 26.94 degrees, the angle to where the plane is now<BR>\n" );
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