document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254435>Question 254435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.)A 12-foot ladder is leaning against the wall. When a painter P was 2/3 of the way of the ladder he dropped his brush which fell directly below him, 1 ft away from the wall. How far was the base of the ladder on the wall?<BR>\n" );
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document.write( "2.)You are flying a kite and have let out 1000 feet of string. The kite string makes a 42º angle with the ground. How high is the kite? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186760 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=186760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 12 foot ladder leaning against a wall.<BR>\n" );
document.write( "painter is 2/3 of the way up when he drops his brush.<BR>\n" );
document.write( "brush lands directly beneath him 1 foot away from the wall.<BR>\n" );
document.write( "how far from the base of the ladder is the wall.\r<BR>\n" );
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document.write( "2/3 of the way up is 8 feet on the ladder.\r<BR>\n" );
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document.write( "diagram of the ladder against the wall is shown below.\r<BR>\n" );
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document.write( "                  A\r\n" );
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document.write( "                  x\r\n" );
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document.write( "                  x     x       4 feet\r\n" );
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document.write( "               F  x x x x x x x x  D\r\n" );
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document.write( "                  x             x           x\r\n" );
document.write( "                  x             x             x     8 feet\r\n" );
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document.write( "                  C             E                       B\r\n" );
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document.write( "A is the point where the ladder touches the wall.<BR>\n" );
document.write( "B is the point where the ladder touches the ground (base of the ladder).<BR>\n" );
document.write( "C is the point where the wall touches the bround (base of the wall).<BR>\n" );
document.write( "D is where the painter is.<BR>\n" );
document.write( "E is where the brush drops<BR>\n" );
document.write( "F is where a line from D parallel to the ground touches the wall.\r<BR>\n" );
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document.write( "you have formed 2 similar triangles.\r<BR>\n" );
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document.write( "they are triangle ABC and triangle ADF\r<BR>\n" );
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document.write( "the distance from C to E on the ground is 1 foot.\r<BR>\n" );
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document.write( "the distance from F to D parallel to the ground is also 1 foot.\r<BR>\n" );
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document.write( "since the triangle are similar, then their corresponding sides are proportional.\r<BR>\n" );
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document.write( "this means that AD / FD = AB / CB\r<BR>\n" );
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document.write( "since AD is 4 feet and AB is 12 feet and FD is 1 foot, this formula becomes:\r<BR>\n" );
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document.write( "4 / 1 = 12 / CB\r<BR>\n" );
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document.write( "cross multiply to get:\r<BR>\n" );
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document.write( "4*CB = 1*12\r<BR>\n" );
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document.write( "divide both sides of this equation by 4 to get:\r<BR>\n" );
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document.write( "CB = 12/4 = 3\r<BR>\n" );
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document.write( "your answer is that the distance from the base of the ladder to the base of the wall is 3 feet.\r<BR>\n" );
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document.write( "kite is 1000 feet long from the flyer of the kite to the kite along the length of the string.\r<BR>\n" );
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document.write( "angle kite makes to the ground is 42 degrees.\r<BR>\n" );
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document.write( "this forms a triangle as shown below:\r<BR>\n" );
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document.write( "                  A\r\n" );
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document.write( "                  x             x  \r\n" );
document.write( "                  x               x   1000 feet\r\n" );
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document.write( "                  x                   x\r\n" );
document.write( "                  x                     x\r\n" );
document.write( "                  x                       x\r\n" );
document.write( "                  x                         x\r\n" );
document.write( "                  x                           x\r\n" );
document.write( "                  x                             x\r\n" );
document.write( "                  x                               x\r\n" );
document.write( "                  x                    42 degrees   x\r\n" );
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document.write( "                  C                                     B\r\n" );
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document.write( "point A is the kite.<BR>\n" );
document.write( "point B is the person flying the kite.<BR>\n" );
document.write( "point C is a point directly beneath the kite perpendicular to the ground.\r<BR>\n" );
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document.write( "the ground is represented by line segment CB\r<BR>\n" );
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document.write( "length of line segment AB is 1000 feet.\r<BR>\n" );
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document.write( "the height of the kite is represwented by line segment AC.\r<BR>\n" );
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document.write( "tangent of 42 degrees = opposite / hypotenuse = AC / AB = AC / 1000\r<BR>\n" );
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document.write( "tan(42) = AC / 1000\r<BR>\n" );
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document.write( "multiply both sides of this equation by 1000 to get:\r<BR>\n" );
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document.write( "1000 * tan(42) = AC = 900.4040443.\r<BR>\n" );
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document.write( "height of the kite is 900.4040443 feet.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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