document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140095>Question 1140095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The angular elevation of a hill at a place P due south of it is 37 degrees and at a place Q due west of P the elevation is 23 degrees. If the distance from P to Q is 3km, find the height of the hill, to the nearest 10 metres </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760627 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=760627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A due south bearing is 180 degrees<BR>\n" );
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document.write( "A due west bearing is 270 degrees<BR>\n" );
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document.write( "Let x be the height of the hill<BR>\n" );
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document.write( "we have two right triangles, let b1 and b2 be the bases of the two triangles<BR>\n" );
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document.write( "tan(37) = x/b1<BR>\n" );
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document.write( "b1 = x/tan(37)<BR>\n" );
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document.write( "similarly<BR>\n" );
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document.write( "b2 = x/tan(23)<BR>\n" );
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document.write( "we have a triangle with two sides equal to x/tan(37) and x/tan(23) and the angle between them is 270 - 180 = 90 degrees<BR>\n" );
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document.write( "ues Pythagorean Theorem<BR>\n" );
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document.write( "(x/tan(37))^2 + (x/tan(23))^2 = 3^2<BR>\n" );
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document.write( "x^2/0.7536^2 + x^2/0.4245^2 = 9<BR>\n" );
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document.write( "x^2/0.5679 + x^2/0.1802 = 9<BR>\n" );
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document.write( "9/x^2 = 1/0.5679 +1/0.1802 = 7.3103<BR>\n" );
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document.write( "x^2 = 9/7.3103 = 1.2311<BR>\n" );
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document.write( "x = 1.1095km = 1109.5m is approximately 1110m<BR>\n" );
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