Question 256426
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Proportionality of Similar Triangles.


You have two similar triangles.  The vertices of the smaller one are the ant, the bottom of the tree, and the top of the tree.  The vertices of the larger one are the ant, the bottom of the building, and the top of the building.


We don't know how far it is from the bottom of the tree to the bottom of the building so let's call that *[tex \Large x].


The distance from the ant to the bottom of the tree is given as 120 ft.  The distance from the ant to the bottom of the building is then *[tex \Large 120\ +\ x].


So, to recap


Height of tree:  80


Height of building: 600


Ant to tree: 120


Ant to building: *[tex \Large 120\ +\ x]


Create the proportion:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{80}{600}\ =\ \frac{120}{120\,+\,x}]


Now all you need to do is cross-multiply and solve.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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