Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
A diagram is shown of a tree to the left of a five-story building.
· A point is marked on the ground to the left of the tree.
· A segment is drawn connecting that point to the top of the tree and then to the top of the building.
· A segment is drawn connecting that point on the ground to the base of the tree and then to the base of the building.
· The part of the segment that connects the point on the ground to the top of the tree and the part that connects the top of the tree to the top of the building are both labeled with a single tick mark.
· The part of the segment that connects the point on the ground to the base of the tree and the part that connects the base of the tree to the base of the building are both labeled with double tick marks.
· The height of the building is labeled as 120 feet.
(1 point)
Responses
60
60
30
30
28
28
120
The information provided does not give enough information to determine the height of the tree.
To determine the height of the tree, we can use similar triangles and proportions. Let's label the height of the tree as 'x'.
Based on the diagram, we can see that the segment connecting the point on the ground to the top of the tree is proportional to the segment connecting the point on the ground to the top of the building. Similarly, the segment connecting the base of the tree to the base of the building is also proportional to the segment connecting the point on the ground to the top of the building.
Using these proportions, we have:
(x + 120)/120 = x/5
To solve for x, we can cross-multiply and solve the equation:
5(x + 120) = 120x
5x + 600 = 120x
115x = 600
x ≈ 5.22
Therefore, the height of the tree is approximately 5.22 feet.
To determine the height of the tree, we can use the concept of similar triangles. In the given diagram, the two triangles formed by connecting the point on the ground, the top of the tree, and the top of the building are similar. This means that their corresponding sides are in proportion.
Using the label given in the diagram, we can see that the distance from the ground to the top of the building (labeled with a single tick mark) is the same as the distance from the ground to the top of the tree.
Since the height of the building is labeled as 120 feet, we can conclude that the height of the tree is also 120 feet.
Therefore, the correct answer is 120.