SOLUTION: Jessica wants to measure the height of a tree. She sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 34 feet from the tree, and Jessica is

Question 1204942: Jessica wants to measure the height of a tree. She sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 34 feet from the tree, and Jessica is standing 10.4 feet from the mirror, as shown in the figure. Her eyes are 5ft above the ground. How tall is the tree? Round your answer to the nearest foot. (The figure is not drawn to scale.)
Answer by ikleyn(52866) (Show Source): You can put this solution on YOUR website!
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Jessica wants to measure the height of a tree. She sights the top of the tree, using a mirror that is lying
flat on the ground. The mirror is 34 feet from the tree, and Jessica is standing 10.4 feet from the mirror,
as shown in the figure. Her eyes are 5ft above the ground. How tall is the tree?
Round your answer to the nearest foot. (The figure is not drawn to scale.)
~~~~~~~~~~~~~~~~~~

For a mirror and light rays, angle of incidence is equal to angle of reflection.


Using this law from Optics (part of Physics), find from the figure two similar right-angled triangles.


From the triangles similarity, write a proportion

     = .        ( <<<---=== the ratios are    )


where x is the height of the tree (your unknown).


From the proportion, find  x =  = 16.3 feet (rounded).

Solved, with all needed explanations.

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To see many other similar solved problems on proportions in Geometry,
see the lesson
- Using proportions to solve word problems in Geometry
in this site.

Learn the subject from there and become the best student in the class.

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