document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196262>Question 1196262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At point \"A\" due east to a hut, the angle of elevation is 45° and at point \"B\" due it's west the angle of elevation is 30°. The distance from point A to B is 10m. Find height of the hut?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829018 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "This is one way to draw out the diagram<BR>\n" );
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document.write( "Segment CD represents the height of the hut<BR>\n" );
document.write( "Let's call it x for now.\r<BR>\n" );
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document.write( "Triangle ACD is a 45-45-90 triangle, aka an isosceles right triangle. <BR>\n" );
document.write( "These types of right triangles have congruent legs.<BR>\n" );
document.write( "We have CD = x and AD = x as those legs.\r<BR>\n" );
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document.write( "AB = 10<BR>\n" );
document.write( "DB = AB - AD<BR>\n" );
document.write( "DB = 10 - x\r<BR>\n" );
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document.write( "Triangle BCD is a 30-60-90 triangle, which means the long leg is exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times that of the short leg.<BR>\n" );
document.write( "Note the short leg of these types of triangles is always opposite the 30 degree angle. The smallest side is opposite the smallest angle.\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=long_leg+=+%28short_leg%29%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"long_leg+=+%28short_leg%29%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DB+=+%28CD%29%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"DB+=+%28CD%29%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-x+=+x%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"10-x+=+x%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+x%2Asqrt%283%29%2Bx ALIGN=MIDDLE  ALT=\"10+=+x%2Asqrt%283%29%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Asqrt%283%29%2Bx+=+10 ALIGN=MIDDLE  ALT=\"x%2Asqrt%283%29%2Bx+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28sqrt%283%29%2B1%29+=+10 ALIGN=MIDDLE  ALT=\"x%28sqrt%283%29%2B1%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10%2F%28sqrt%283%29%2B1%29 ALIGN=MIDDLE  ALT=\"x+=+10%2F%28sqrt%283%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is one way to express the exact height.<BR>\n" );
document.write( "Another way is to rationalize the denominator.\r<BR>\n" );
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document.write( "Use a calculator to find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%28sqrt%283%29%2B1%29+=+3.66025 ALIGN=MIDDLE  ALT=\"10%2F%28sqrt%283%29%2B1%29+=+3.66025\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately\r<BR>\n" );
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document.write( "Answer: The height is roughly 3.66025 meters\r<BR>\n" );
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document.write( "Similar question:<BR>\n" );
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