document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=418669>Question 418669</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tree on a hillside casts a shadow c ft down the hill. If the angle of inclination of the hillside is b to the horizontal and the angle of elevation of the sun is a, find the height of the tree. Assume a = 57°, b = 27° c = 240 ft. (Round your answer to the nearest whole number.)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293106 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=293106\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A tree on a hillside casts a shadow c ft down the hill. If the angle of inclination of the hillside is b to the horizontal and the angle of elevation of the sun is a, find the height of the tree. Assume a = 57°, b = 27° c = 240 ft. (Round your answer to the nearest whole number.)\r<BR>\n" );
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document.write( "Draw a hillside that is inclined 27 deg to the horizontal(from right to left).<BR>\n" );
document.write( "Someplace on the surface of the hill draw a vertical line (to the horizontal)which represents the height of the tree. From the top of this vertical line we will call point A, draw a line down to the surface of the hill at point B. This is a 33 deg. angle the sun makes with the surface of the hillside. The bottom of the vertical line to point B along the surface is given to be 240 ft.which is the shadow of the tree. Extend the bottom (point D) of the vertical line into the hillside,then at a point we will call C, turn at a right angle to extend this line to point B. We now have two triangles to work with,ABC, a right triangle with angle at B=57 deg. and BCD, a right triangle with angle at B=27 deg., both sharing leg BC.<BR>\n" );
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document.write( "Calculations:\r<BR>\n" );
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document.write( "Height of tree=AC-DC=AD<BR>\n" );
document.write( "DC/240=Sin 27 deg<BR>\n" );
document.write( "DC=240*Sin 27 deg=108.96 ft<BR>\n" );
document.write( "AC/CB=tan 57 deg<BR>\n" );
document.write( "AC=CB*tan 57 deg<BR>\n" );
document.write( "CB/240=Cos 27 deg<BR>\n" );
document.write( "CB=240*Cos 27 deg=213.84 ft<BR>\n" );
document.write( "AC=213.84*tan 57 deg=329.28 ft<BR>\n" );
document.write( "AD=AC-DC=329.28-108.96=220 ft<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "Height of tree=220 ft\r<BR>\n" );
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document.write( "An alternative solution:<BR>\n" );
document.write( "Find the angles at A, B & D<BR>\n" );
document.write( "At B, it is 57-27=30 deg.<BR>\n" );
document.write( "At A, it is 33 deg.<BR>\n" );
document.write( "sin 30/AD=sin 33/240<BR>\n" );
document.write( "AD=240*SinB/sinA=240*sin30/sin33=220 ft\r<BR>\n" );
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