a tree that is 22 meters tall, casts a shadow of 28 meters. a building located nearby cast a shadow of 56 meters. what is the height of the building?
height / shadow length = 22 / 28 = h / 56
so
h = 56 * (22 / 28)
To determine the height of the building, we can use a proportion based on the similar triangles formed by the tree and its shadow, and the building and its shadow.
Let's set up the proportion:
Height of the tree / Length of the tree's shadow = Height of the building / Length of the building's shadow
Plugging in the values we have:
22 meters (height of the tree) / 28 meters (length of the tree's shadow) = Height of the building / 56 meters (length of the building's shadow)
Now, let's solve for the height of the building:
Cross multiplying, we get:
22 * 56 = 28 * Height of the building
Therefore, 1232 = 28 * Height of the building
Finally, divide both sides by 28:
Height of the building = 1232 / 28
Simplifying the division:
Height of the building ≈ 44 meters
So, the height of the building is approximately 44 meters.
To find the height of the building, we can use similar triangles. In this case, the ratio of the tree's height to its shadow length should be equal to the ratio of the building's height to its shadow length. We can set up the following proportion:
Tree's height / Tree's shadow = Building's height / Building's shadow
Plugging in the given values:
22 / 28 = Building's height / 56
To solve for the building's height, we can cross-multiply and solve for the unknown value:
22 * 56 = Building's height * 28
1232 = Building's height * 28
Dividing both sides by 28:
Building's height = 1232 / 28
Simplifying this:
Building's height = 44 meters
Therefore, the height of the building is 44 meters.