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.
Determine the height of the flagpole. Express your answer to the nearest tenth of a
foot.
Solve the proportion:
height/85 = 6.5/9.75
To determine the height of the flagpole, we can set up a proportion between the height of the flagpole and the height of the basketball player.
Let's denote:
- h as the height of the flagpole
- d as the distance from the base of the flagpole to its shadow
From the given information:
- The shadow of the flagpole measures 85 ft., so d = 85 ft.
- The height of the basketball player is 6.5 ft., and their shadow measures 9.75 ft.
Using the concept of similar triangles, which states that corresponding angles in similar triangles are equal, we can set up the following proportion:
(height of flagpole) / (distance from base to shadow of flagpole) = (height of basketball player) / (distance from base to shadow of basketball player)
h / d = 6.5 / 9.75
Now, we can substitute the given values into the equation:
h / 85 = 6.5 / 9.75
To solve for h, we can cross-multiply:
h * 9.75 = 6.5 * 85
h * 9.75 = 552.5
Finally, divide both sides by 9.75 to isolate h:
h = 552.5 / 9.75
Calculating this value yields:
h ≈ 56.6 ft.
Therefore, the height of the flagpole is approximately 56.6 feet.