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Question

Shanice wants to determine the height of a tree in a field. She measures the tree’s shadow to be 36 feet long. Then she stands next to the tree and measures her own shadow to be 3 feet long. She knows that she is 5 feet tall. Using similar triangles, find the height of the tree to the nearest foot.

Answer 1

Using the similar triangles formed by Shanice's shadow and the tree's shadow, we can set up a proportion to solve for the height of the tree.

Let x be the height of the tree.

We have the proportion:

(tree's height) / (tree's shadow length) = (Shanice's height) / (Shanice's shadow length)

x / 36 = 5 / 3

Cross multiply:

3x = 180

x = 60

Therefore, the height of the tree is 60 feet.