Use the image to answer the 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.
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.