Samantha wants to find the height of a pine tree on her yard.she measures the heigth of the mailbox at tree feet and it shadow at 4.8 feet. Then she measures the shadow of the tree at 56 feet . How tall is the tree?
3/4.8 = x/56
Cross multiply and solve for x.
To find the height of the tree, Samantha can use a method called similar triangles. Similar triangles are triangles that have the same shape, but possibly different sizes.
In this case, Samantha can set up a proportion using the height of the mailbox (3 feet), the length of its shadow (4.8 feet), the length of the tree's shadow (56 feet), and the unknown height of the tree (let's call it x feet).
The proportion can be set up as follows:
(height of mailbox) / (length of mailbox's shadow) = (height of tree) / (length of tree's shadow)
or
3 / 4.8 = x / 56
To solve for x, Samantha can cross-multiply and then divide:
3 * 56 = 4.8 * x
168 = 4.8 * x
Dividing both sides by 4.8:
168 / 4.8 = x
35 = x
Therefore, the tree is 35 feet tall.