A flagpole casts a shadow 27 feet long. At the same time of day, a person standing nearby casts a shadow of 8 feet long. If the person is 6 feet tall, how tall is the flagpole?
geometry, not geography.
Draw a diagram. It should be clear that the height h can be found via
h/27 = 6/8
To find the height of the flagpole, we can use similar triangles. The length of the person's shadow can be considered as the height of the person while the length of the flagpole's shadow represents the height of the flagpole.
Let's define some variables:
Let x be the height of the flagpole.
We can set up the following proportion to solve for x:
(height of flagpole) / (length of flagpole's shadow) = (height of person) / (length of person's shadow)
Plugging in the given values:
x / 27 = 6 / 8
We can cross multiply and solve for x:
8x = 27 * 6
8x = 162
x = 162 / 8
x = 20.25
Therefore, the height of the flagpole is 20.25 feet.