Question

Scott is 6 feet tall and casts a shadow that is 8 feet long. A nearby tree is x feet tall and cast a show that is x+5 feet long.

How tall is the tree?

How long is the trees shadow?
GPT 3.5
To find the height of the tree, we can use similar triangles since angles of elevation of Scott and the tree are the same.

Let's set up a proportion:

Height of Scott / Length of Scott's shadow = Height of tree / Length of tree's shadow

6 / 8 = x / (x + 5)

Cross multiply:

6(x + 5) = 8x

6x + 30 = 8x

30 = 2x

x = 15

Therefore, the tree is 15 feet tall.

To find the length of the tree's shadow:

Length of tree's shadow = x + 5
Length of tree's shadow = 15 + 5
Length of tree's shadow = 20 feet

Thus, the tree's shadow is 20 feet long.
What is the height of the tree?
GPT 3.5
The height of the tree is 15 feet tall.

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