Amy is 5 feet tall. She places a mirror on the ground and moves until she can see the top of a nearby tree. At this point, she is 2 feet from the mirror. the tree is 48 feet from the mirror. How tall is the tree?

120ft

48 / 2 = x / 5

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To find the height of the tree, we can use similar triangles and the concept of proportions.

Let's denote the height of the tree as "h" feet.

Using the information provided, we have a right triangle formed by Amy, the mirror, and the top of the tree:

Amy
| /|
| / |
| / |h
| / |
|/_____________
Mirror Tree

From the triangle, we can form two similar triangles:

1. Triangle formed by Amy's height, distance from Amy to mirror, and distance from mirror to the base of the tree.
2. Triangle formed by the height of the tree, distance from tree to mirror, and distance from mirror to the base of the tree.

Let's set up a proportion between the corresponding sides of these triangles:

Amy's height / Distance from Amy to mirror = Height of tree / Distance from tree to mirror

Using the given values:
5 feet (Amy's height) / 2 feet (Distance from Amy to mirror) = h feet (Height of tree) / 48 feet (Distance from tree to mirror)

Now, we can solve for the height of the tree (h):

Cross-multiplying the proportions, we have:
(5 feet) * (48 feet) = (2 feet) * h

240 feet = 2h

Finally, divide both sides of the equation by 2:

h = 240 feet / 2
h = 120 feet

Therefore, the height of the tree is 120 feet.