# The Problem

In the late afternoon, a person who is 6 feet
tall casts a shadow 15 feet long. If the top of their shadow is
at the same point on the ground as the top of the shadow of a
50 foot tree, how far is the man from standing from the base of
the tree?

### (Source: Adapted from Mathematics Teaching in the
Middle School, Sep1995).

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# The Solution

### We can solve this problem using the ratio relationship between
similar triangles. The figure make triangles, and since the smaller
triangle shares a vertex with the larger triangle, and they are
both right trianlges they are similar. The relationship between
the objects can be better understood looking at the picture below:

###

###

### We can solve for the missing distance by setting up a ratio
and solving for the unknown side:

### 6ft/50ft = 15ft/x

### We can cross multiply and develop the following equation:

### 6x = 750

### x= 125 feet

### So we can see that the tree's shadow is 125 long.