what is the height of the flagpole?

Question

A person who is 6 feet tall walks away from a flagpole toward the tip of the shadow of the flagpole. When the person is 28 feet from the flagpole, the tips of the person's shadow and the shadow cast by the flagpole coincide at a point 7 feet in front of the person.

Answer 1

Hi Nick, working with similar triangles, we can find the height of the flagpole.

 

Start with the person and their shadow. The person is 6 feet tall and casts a shadow of 7 feet, the height and base of the triangle.

 

 

The person walks 28 feet away from the flagpole and their shadow matches the shadow of the flagpole. The flagpole has a shadow length of 28 + 7 feet.

 

Let x be the height of the flagpole with a base of 35 feet.

 

The ration of the person and their shadow to the flagpole and its shadow is:

 

7 / 6 :: 35 (this is 28 + 7) / x

 

Cross multiply gives:

 

7x = 210

 

Divide both sides by 7:

 

x = 30

 

The height of the flagpole is 30 feet.

 

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