How tall is the flag pole?

Joe wants to find the height of a pole. Beginning at the pole, Joe walks 25 feet along the shadow that the pole casts until his shadow ends at the same point as the pole's shadow. Joe is 6-feet tall and his shadow is 9-feet long. How tall is the pole?

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Two similar triangles are created.....the triangle of the flag pole and its shadow as well as the triangle of Joe and his shadow.

Since the two triangles are similar, the sides are proportional.

Set up a proportion:

  Joe's height               Joe's shadow
---------------  =  ------------------
flag pole height      flag pole shadow

     6                  9
-------  =  --------
     x                  25

9x = 150   {cross-multiplied}

x ≈ 16.7 feet  {divided and rounded}

The flag pole is approximately 16.7 feet tall.

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