Question 1048375
.
To determine the height AB of a tree, Nancy places a mirror on the ground at E. From E, she walks backwards to a point D, 
where she is just about to see the top of the tree in the mirror. Given BE=18m, ED=2.4m, angle CED = angle AEB, 
and that her eyes are 1.6 m off the ground, find the height of the tree.

The answer is 12m, I don't get how!
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<pre>
Make a sketch, please.

The point B is on the ground, where the tree is standing.
The point A is the top of the tree.

The point D is on the ground, where Nancy is standing.
The point C is where Nancy's eyes are.

The triangles BAE and DCE are similar.
Why? They are right-angled triangles, and, in addition, you are given that
angle CED = angle AEB.  (The last is the Reflection Law for a mirror).

Since the triangles are similar, their corresponding sides are proportional:

{{{abs(AB)/abs(BE)}}} = {{{abs(CD)/abs(DE)}}}.

Substitute the given data. You will get

{{{abs(AB)/18}}} = {{{1.6/2.4}}}.

Find the unknown value of |AB| from this proportion.

|AB| = {{{(18*16)/2.4}}} = 12 m (coincides with your answer !)

Now you know why.
</pre>

On triangles similarity, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/Similar-triangles.lesson>Similar triangles</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/Similarity-tests-for-triangles.lesson>Similarity tests for triangles</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/Proofs-of-Similarity-tests-for-triangles.lesson>Proofs of Similarity tests for triangles</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/In-a-triangle-a-straight-line-parallel-to-its-side-cuts-off-a-similar-triangle.lesson>In a triangle a straight line parallel to its side cuts off a similar triangle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/Problems-on-similar-triangles.lesson>Problems on similar triangles</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/Similarity-tests-for-right-angled-triangles.lesson>Similarity tests for right-angled triangles</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/Problems-on-similarity-for-right-angled-triangles.lesson>Problems on similarity for right-angled triangles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/Problems-on-similarity-for-right-angled-and-acute-triangles.lesson>Problems on similarity for right-angled and acute triangles</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/One-property-of-a-median-in-a-triangle.lesson>One property of a median in a triangle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/One-property-of-a-trapezoid.lesson>One property of a trapezoid</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Triangles/Miscellaneous-problems-on-similar-triangles.lesson>Miscellaneous problems on similar triangles</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-similar-triangles.lesson>Solved problems on similar triangles</A> 

in this site.