Samantha wants to find the height of a pine tree in her yard. She measures the height of the mailbox at 3 feet and its shadow at 4.8 feet. Then she measures the shadow of the tree at 56 feet. How tall is the tree?
89.6
89.6
To find the height of the tree, we can use the concept of similar triangles. Let's assume that the height of the tree is "h" feet.
We have two triangles: the triangle formed by the mailbox, its shadow, and the tree's shadow; and the triangle formed by the mailbox, its height, and the tree's height.
Using the concept of similarity, we can set up the following proportion:
(mailbox shadow)/(mailbox height) = (tree shadow)/(tree height)
Plugging in the given values, we have:
4.8/3 = 56/h
To solve for "h," we can cross multiply and then divide:
4.8h = 3 * 56
4.8h = 168
h = 168 / 4.8
h ≈ 35
Therefore, the height of the tree is approximately 35 feet.
3/4.8 = x/56
Cross multiply and solve for x.