A tree stands 22 feet tall and is 382 feet from a building. The tree casts a shadow that is 40 feet long. How tall is the building?
Make a sketch and use a simple ratio:
22/h = 40/(40+382)
40h = 22(40+382) = 9284
h = 232.1 ft
Thank you!
To determine the height of the building, we can use the concept of similar triangles.
First, let's identify the corresponding sides of the two triangles formed by the tree, its shadow, and the building:
1. The height of the tree corresponds to the height of the building.
2. The length of the tree's shadow corresponds to the distance between the tree and the building.
Now, we can set up a proportion between the corresponding sides of the triangles:
(tree height) / (tree shadow length) = (building height) / (distance from the tree to the building)
Substituting the given values:
(22 feet) / (40 feet) = (building height) / (382 feet)
To solve for the height of the building, we can cross-multiply and solve the resulting equation:
(22 feet) * (382 feet) = (40 feet) * (building height)
8,404 square feet = 40 feet * (building height)
Dividing both sides by 40 feet:
(8,404 square feet) / (40 feet) = building height
210.1 feet = building height
Therefore, the height of the building is approximately 210.1 feet.