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If a flagpole has a shadow 56 feet long when a 6 foot man's shadow is 14 feet long, what is the height of the flagpole?

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If a flagpole has a shadow 56 feet long when a 6 foot man's shadow is 14 feet long, what is the height of the flagpole?

ranga · Answer

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anonymous · Answer

Solve the following for x:$$\frac{6}{14}=\frac{x}{56} $$

ranga · Answer

The two triangles are similar.  Therefore, their sides are proportional.

calculusxy · Answer

x=24.
How did you know that you had to do a proportion and set up the numerator and denominator that way? @robtobey

calculusxy · Answer

@shamil98 @ranga

ranga · Answer

The sun or light rays are falling at the same angle on the man and the flag pole.  So AC and DF are parallel.  Both the man and the flagpole are straight up and so AB and DE are parallel.  Both shadows fall on the ground.  So BC and EF are along the same line.  Therefore, the triangles are similar and their sides are proportional.

anonymous · Answer

@calculusxy

Mentally used @ranga's illustrations from experience.