A person who is 6
feet tall is standing 132
feet from the base of a tree, and the tree casts a 144
foot shadow. The person's shadow is 12
feet in length. What is the height of the tree?
Let's call the height of the tree "h".
We can set up a proportion using similar triangles formed by the person, the person's shadow, the tree, and the tree's shadow:
(person's height) / (person's shadow length) = (tree's height) / (tree's shadow length)
Plugging in the values we know:
6 / 12 = h / 144
Simplifying:
1/2 = h / 144
Multiplying both sides by 144:
h = 72
Therefore, the height of the tree is 72 feet.
To find the height of the tree, we can use a proportion based on the given information.
Let's represent the height of the tree as 'h'.
According to the given information, the person is 6 feet tall and is standing 132 feet from the base of the tree. The person's shadow is 12 feet in length, while the tree's shadow is 144 feet.
So, we can set up the proportion:
(person's height) / (person's shadow) = (tree's height) / (tree's shadow)
Substituting the given values:
6 / 12 = h / 144
To solve for 'h', we can cross multiply:
6 * 144 = 12 * h
864 = 12h
Divide both sides by 12 to isolate 'h':
h = 864 / 12
h = 72
Therefore, the height of the tree is 72 feet.