document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044038>Question 1044038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From the stage of a theater, the angle of elevation to the first balcony is 19 degrees. The angle of elevation to the second balcony, 6.3 meters directly above the first, is 29 degrees. How high above stage level is the first balcony, to the nearest tenth of a meter?\r<BR>\n" );
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document.write( "a. 8.5 meters<BR>\n" );
document.write( "b. 10.3 meters<BR>\n" );
document.write( "c. 12.4 meters<BR>\n" );
document.write( "d. 14.2 meters<BR>\n" );
document.write( "e. 16 meters </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659270 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the horizontal distance to the first balcony (a leg of the triangle) x.<BR>\n" );
document.write( "Then the height of the balcony from that spot is h.<BR>\n" );
document.write( "tangent of y=h/x<BR>\n" );
document.write( "x=h/tan 19<BR>\n" );
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document.write( "To the second balcony, it will be x=(h+6.3)/tan 29<BR>\n" );
document.write( "Set the two equal to each other since they are both equal to x.<BR>\n" );
document.write( "h/tan 19=(h+6.3/tan 29<BR>\n" );
document.write( "cross-multiply<BR>\n" );
document.write( "h tan 29=(h+6.3) tan 19=h tan 19+6.3 tan 19<BR>\n" );
document.write( "h tan 29-h tan 19=6.3 tan 19=2.17<BR>\n" );
document.write( "h(tan 29-tan 19)=2.17<BR>\n" );
document.write( "0.21 h=2.17 i<BR>\n" );
document.write( "h=10.3 m ANSWER IS A<BR>\n" );
document.write( "Check using 10.33, the answer to two decimal places<BR>\n" );
document.write( "x, the horizontal distance, is 30 m.<BR>\n" );
document.write( "10.33/30=0.3433, and tan ^(-1) of  that is 19.00 degrees<BR>\n" );
document.write( "16.33/30=0.5543  and tan ^(-1) of that is  29.00 degrees. <BR>\n" );
document.write( " </SPAN>\n" );
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