when james planted a tree 5 m from a window the tree just blocked from view a building 50 m away if the building was 20 m tall how tall was the tree?
To determine the height of the tree, we need to make use of similar triangles and apply the concept of triangle proportionality theorem.
Let's denote:
- h as the height of the tree,
- d as the distance from the window to the tree,
- D as the distance from the window to the building.
According to the given information, James planted the tree 5 meters away from the window, and the tree blocked the view of a 50-meter distant building. We can set up the following proportions based on the similar triangles:
h/20 = (h + 5)/50
By cross-multiplying this proportion, we get:
50h = (h + 5) * 20
Expanding and simplifying the equation:
50h = 20h + 100
Subtracting 20h from both sides:
50h - 20h = 100
Simplifying further:
30h = 100
Dividing both sides by 30:
h = 100 / 30
Therefore, the height of the tree is approximately 3.33 meters.