A man 6 feet tall casts a shadow 4 feet long at the same time when a flagpole casts a shadow 50 feet long. The height of the flag pole is?

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Detailed Solution

Let's take into consideration a figure that reflects the heights and shadows of both the guy and the flag post based on the information provided in the inquiry. It appears as two triangles as seen below:
Question Image

The man's height is represented by the side DE, and his shadow by AE. The side BC represents the flag post's height, and the side AC represents its shadow. The flag post and the man are both vertically up from the ground.
We can now conclude from the figure that ∆ADE and ∆ABC appear as two related triangles. Therefore, we can assert that the corresponding sides of both triangles are in proportion by applying the property of corresponding sides of similar triangles.
As a result, we can state:
⇒ [Equation] ⇒ [Equation] ⇒ [Equation] ⟹ [Equation].
Consequently, the flagpole is [Equation] feet tall.

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