Use similar triangles to solve. A person who is 6 feet tall is standing 81 feet from the base of a tree, and the tree casts a 90 foot shadow. The person's shadow is 9 feet in length. What is the height of the tree?
Let x be the height of the tree.
Since the person's height and the tree's height form the legs of similar right triangles (person-tree and person-shadow), we can set up the following proportion:
6/x = 9/90
Cross multiplying, we get:
6 * 90 = 9x
540 = 9x
x = 540/9
x = 60
Therefore, the height of the tree is 60 feet.