The sun causes a flagpole to cast a shadow that measures 85 ft. from the base of the pole. At the same time of the day, a 6.5 ft. tall basketball player casts a shadow that measures 9.75 ft. Set up a proportion to solve for the height of the flagpole in this problem
f / 85 = 6.5 / 9.75
To set up a proportion to solve for the height of the flagpole, we can compare the ratios of the heights of the objects to the lengths of their shadows.
Let's assign the following variables:
Height of the flagpole: F (what we want to find)
Height of the basketball player: B = 6.5 ft.
Length of the flagpole's shadow: Sf = 85 ft.
Length of the basketball player's shadow: Sb = 9.75 ft.
The proportion can be set up as follows:
F / B = Sf / Sb
Substituting the given values:
F / 6.5 = 85 / 9.75
We can solve this proportion by cross-multiplying and then dividing:
F * 9.75 = 6.5 * 85
F * 9.75 = 552.5
F = 552.5 / 9.75
Using a calculator, we can find that F is approximately 56.67 ft.
Therefore, the height of the flagpole is approximately 56.67 ft.