document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170350>Question 1170350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Have no idea where to even begin to solve this problem. Any help is appreciated.\r<BR>\n" );
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document.write( "The Grand Canyon Skywalk at Eagle Point is a horseshoe shaped steel frame with a glass floor looking down to the Grand Canyon below.  The Skywalk extends 70 feet over the canyon rim and is 10 feet wide.  The walkway consists of a semicircle with a straight portion on each side<BR>\n" );
document.write( "Path Width 10 feet 65 feet Outer Circle: 65 feet diameter Location of Light Tower .Inner Circle. 45 feet diameter 70 feet\r<BR>\n" );
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document.write( "A light tower is going to be installed on the left edge of the Skywalk .<BR>\n" );
document.write( "The light will shine down to the opposite edge of the Skywalk <BR>\n" );
document.write( " How tall does the light tower need to be if the angle of depression is 51°?  (Round to 1 decimal place and be sure to include units.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851212 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem step-by-step.\r<BR>\n" );
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document.write( "**1. Understand the Geometry:**\r<BR>\n" );
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document.write( "* The Skywalk has a semicircular section and two straight sections.<BR>\n" );
document.write( "* We're interested in the distance across the Skywalk where the light will shine.<BR>\n" );
document.write( "* The light tower is on the left edge, and the light shines to the right edge.<BR>\n" );
document.write( "* The angle of depression is given, and we need to find the height of the tower.\r<BR>\n" );
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document.write( "**2. Calculate the Total Width of the Skywalk:**\r<BR>\n" );
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document.write( "* The semicircle has an outer diameter of 65 feet.<BR>\n" );
document.write( "* The straight portions are each 70 feet long.<BR>\n" );
document.write( "* The total width from left to right is therefore the diameter of the semicircle.<BR>\n" );
document.write( "* The width of the skywalk is 65 feet.\r<BR>\n" );
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document.write( "**3. Set Up the Trigonometry:**\r<BR>\n" );
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document.write( "* We have a right triangle formed by:<BR>\n" );
document.write( "    * The height of the light tower (opposite side).<BR>\n" );
document.write( "    * The width of the Skywalk (adjacent side).<BR>\n" );
document.write( "    * The line of sight of the light beam.<BR>\n" );
document.write( "* The angle of depression is the angle between the horizontal and the line of sight. It's equal to the angle of elevation from the bottom of the triangle.<BR>\n" );
document.write( "* We'll use the tangent function:<BR>\n" );
document.write( "    * tan(angle) = opposite / adjacent\r<BR>\n" );
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document.write( "**4. Solve for the Height:**\r<BR>\n" );
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document.write( "* tan(51°) = height / 65 feet<BR>\n" );
document.write( "* height = 65 feet * tan(51°)<BR>\n" );
document.write( "* tan(51°) ≈ 1.2349<BR>\n" );
document.write( "* height ≈ 65 feet * 1.2349<BR>\n" );
document.write( "* height ≈ 80.2685 feet\r<BR>\n" );
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document.write( "**5. Round to One Decimal Place:**\r<BR>\n" );
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document.write( "* The height of the light tower is approximately 80.3 feet.\r<BR>\n" );
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document.write( "**Final Answer:** The light tower needs to be approximately 80.3 feet tall.<BR>\n" );
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