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?

1 answer

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.