A tree is 38.5 feet tall casts a shadow that is 9 feet 4 inches long.A utility pole beside the tree casts a shadow that is sixty-four inches long.Find the height of the utility pole. Show work
Set up a proportion. Cross multiply and solve for x.
38.5/9.33 = x/5.33
9.333x = 205.33333
x = 22 feet
A tree is 3 times as tall as a nearby pole. If the tree is 14 feet 9 inches tall, how tall is the pole?
To find the height of the utility pole, we can use a proportional relationship between the height of the tree and the length of its shadow, and the height of the utility pole and the length of its shadow.
First, let's convert the measurements to feet for easier calculations:
The height of the tree is 38 feet and 6 inches. Since 1 foot is equal to 12 inches, we can convert the inches to feet by dividing 6 by 12. This gives us 0.5 feet. Therefore, the height of the tree is 38.5 feet.
The length of the tree's shadow is 9 feet and 4 inches. Following the same process, we convert the inches to feet by dividing 4 by 12. This gives us 0.33 feet. Therefore, the length of the tree's shadow is 9.33 feet.
The length of the utility pole's shadow is 64 inches. Similarly, we divide 64 by 12 to convert it to feet. This gives us 5.33 feet.
Now, we can set up the proportion:
Height of tree / Length of tree's shadow = Height of utility pole / Length of utility pole's shadow
Substituting the values we have:
38.5 feet / 9.33 feet = Height of utility pole / 5.33 feet
To find the height of the utility pole, we cross-multiply:
38.5 feet * 5.33 feet = 9.33 feet * Height of the utility pole
205.8055 square feet = 9.33 feet * Height of the utility pole
Solving for the height of the utility pole:
Height of the utility pole = 205.8055 square feet / 9.33 feet
Height of the utility pole ≈ 22.05 feet