Estimating the Height of a Building

<BODY LANG="EN" > <HR><center> <table border=1> <td><A HREF="node67.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node67.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node69.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node68.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR> <H3>Estimating the Height of a Building</H3> <P> <CENTER> <IMG SRC="p11-1.gif" WIDTH=176 HEIGHT=65 ALT="[figure]"> </CENTER> <P> Consider the problem of calculating the height of a building. As a student stands outside the building, she wonders how she will accomplish such a task without a <B>really</B> long tape measure! She then remembers she has a protractor and performs the following calculations: <P> She notes that, at a distance of 10 feet from the building, the angle of elevation is <nobr>75°.</nobr> This is all the information she needs to estimate the height of the building. How will she accomplish this? <P> She draws the following figure: <P> <CENTER> <IMG SRC="p11-2.gif" WIDTH=97 HEIGHT=80 ALT="[figure]"> </CENTER> <P> Then she notes that, since <IMG WIDTH=89 HEIGHT=36 ALIGN=MIDDLE ALT="tan 75 = y/10" SRC="img205.gif">, she can solve for <I>y</I> as <IMG WIDTH=104 HEIGHT=24 ALIGN=MIDDLE ALT="y = 10 tan 75" SRC="img206.gif"> This leaves her with just one job: calculating <IMG WIDTH=47 HEIGHT=12 ALIGN=BOTTOM ALT="tan 75" SRC="img207.gif">. She can calculate this using the sum formula for <IMG WIDTH=21 HEIGHT=10 ALIGN=BOTTOM ALT="tan" SRC="img22.gif">. <P> <CENTER> <IMG WIDTH=244 HEIGHT=182 ALIGN=BOTTOM ALT="[calc of tan 75]" SRC="img208.gif"> </CENTER> <P> Therefore, she knows that <IMG WIDTH=118 HEIGHT=24 ALIGN=MIDDLE ALT="y ~ 10 x 3.73205" SRC="img209.gif"> or 37.3205 feet. <P> <HR><center> <table border=1> <td><A HREF="node67.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node67.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node69.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node68.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I><A HREF="http://www.math.psu.edu/sellersj/">James A. Sellers</A> </I> </ADDRESS> </BODY>