document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092478>Question 1092478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The angle of depressions of a car on the ground from the top of a building is 72°.If the car is 200 feet away from the building.Find the height of the building?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707103 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the car and the building form a right triangle.\r<BR>\n" );
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document.write( "call this triangle ABC.\r<BR>\n" );
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document.write( "A is the lower left hand corner.<BR>\n" );
document.write( "B is the upper left hand corner.<BR>\n" );
document.write( "C is the lower right hand corner.\r<BR>\n" );
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document.write( "angle B is 72 degrees.<BR>\n" );
document.write( "angle A is 90 degrees.<BR>\n" );
document.write( "angle C is 18 degrees.\r<BR>\n" );
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document.write( "AC is equal to 200 feet.\r<BR>\n" );
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document.write( "you want to find the length of AB\r<BR>\n" );
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document.write( "tan(B) is equal to opposite / adjacent = 200 / AB\r<BR>\n" );
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document.write( "solve for AB to get AB = 200 / tan(B) = 200 / tan(72)\r<BR>\n" );
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document.write( "cot(C) is equal to adjacent / opposite = 200 / AB\r<BR>\n" );
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document.write( "solve for AB to get AB = 200 / cot(C) = 200 / cot(18)\r<BR>\n" );
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document.write( "you can use your calculator to solve.\r<BR>\n" );
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document.write( "200 / tan(72) = 64.98393925 feet.\r<BR>\n" );
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document.write( "200 / cot(18) = 200 / (1 / tan(18) = 200 * tan(18) = 64.98393925 feet.\r<BR>\n" );
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document.write( "either way you get AB = 64.98393925 feet.\r<BR>\n" );
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document.write( "you can also solve for the distance between the car and the top of the building.\r<BR>\n" );
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document.write( "that would be based on:\r<BR>\n" );
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document.write( "sin(B) = opp / hyp = 200 / BC\r<BR>\n" );
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document.write( "solve for BC to get BC = 200 / sin(B) = 200 / sin(72) = 210.2924448.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "AB = 64.98393925<BR>\n" );
document.write( "AC = 200<BR>\n" );
document.write( "BC = 210.2924448\r<BR>\n" );
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document.write( "by pythagorus, BC^2 = AB^2 + AC^2\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "210.2924448^2 = 64.98393925^2 + 200^2\r<BR>\n" );
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document.write( "simplify to get 44222.91236 = 4222.91236 + 40000.\r<BR>\n" );
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document.write( "combine like terms to get 44222.91236 = 43222.91236\r<BR>\n" );
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document.write( "the formula is true and so the measurements of AB and AC and BC are true.\r<BR>\n" );
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document.write( "solution to your problem is that the height of the building is equal to 64.98393925 feet.\r<BR>\n" );
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document.write( "round as required.\r<BR>\n" );
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