what is the function of the following table: a tree that has a height of 12 feet will have a shadow of 10 feet
The table you are referring to represents the relationship between the height of a tree and the length of its shadow. In this specific case, it states that a tree with a height of 12 feet will have a shadow that is 10 feet in length.
To understand the function of this table, we can interpret it as a direct proportion. Direct proportion means that as one quantity increases, the other quantity also increases, maintaining a consistent ratio.
In this case, as the height of the tree increases, the length of its shadow also increases. Specifically, for every 1 unit increase in the height of the tree, the shadow length increases by 10/12 units. Since the ratio between the height and shadow length is constant (10/12), we can use this proportion to find the length of the shadow for any given height of the tree.
For example, if you want to determine the shadow length of a tree with a height of 15 feet, you can set up the following proportion:
Height of the first tree / Length of its shadow = Height of the second tree / Length of its shadow
12 feet / 10 feet = 15 feet / x
Solving for x (which represents the length of the shadow for the tree with a height of 15 feet), you can cross-multiply and find that x = (15 * 10) / 12 = 12.5 feet.
Therefore, by using the information provided in the table and understanding the concept of direct proportion, you can determine the shadow length of a tree for different heights.