document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=559509>Question 559509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Brooke wanted to measure the height of the tree in her backyard. Brooke placed the mirror on the ground 32 ft. away from the tree and then walked backwards until she was able to see the top of the tree in the mirror. Her eyes are 5 ft. above the ground and she is 8 ft. from the mirror. Using similar triangles, find the height of the tree. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363449 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That tree is 20 feet tall.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C150%2C-36%2C12%2C-2%2C22%2C%0D%0Agreen%28triangle%28-32%2C0%2C-32%2C20%2C0%2C0%29%29%2C%0D%0Ablue%28triangle%288%2C0%2C8%2C5%2C0%2C0%29%29%2C%0D%0Aline%28-34%2C0%2C-32%2C0%29%2Cline%288%2C0%2C12%2C0%29%2C%0D%0Ared%28line%28-0.5%2C0%2C0.5%2C0%29%29%2C%0D%0Alocate%280%2C0%2CM%29%2C%0D%0Alocate%288%2C0%2CF%29%2Clocate%288%2C7%2CE%29%2C%0D%0Alocate%28-16%2C2.2%2C32%29%2Clocate%284%2C2.2%2C8%29%2Clocate%288.3%2C3%2C5%29%2C%0D%0Alocate%28-32%2C0%2CR%29%2C+locate%28-32%2C22%2CT%29%2Clocate%28-32.5%2C10%2Ctree%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The tree (RT, Root to Top) and Brooke (FE, Feet to Eye) are the short legs of similar right triangles MRT and MFE. (The ground, and red mirror M are perfectly level and horizontal. The green tree and blue-eyed Brooke stand perfectly straight, vertical, and perpendicular to the ground. As a consequence the angles at R and F are right angles, and therefore congruent to each other. The mirror reflects symmetrically, so the angles at M are congruent too. That makes the remaining pair of angles (at T and E) congruent, and the triangles similar).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MR%2FMF=32%2F8=4 ALIGN=MIDDLE  ALT=\"MR%2FMF=32%2F8=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All the sides'lengths in MRT are 4 times the length of the corresponding sides in MFE. So RT is 4 times FE, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A5 ALIGN=MIDDLE  ALT=\"4%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20. </SPAN>\n" );
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