Use similar triangles to solve. A person who is 6 feet tall is standing 140 feet from the base of a tree, and the tree casts a 154 foot shadow. The persons shadow is 14 feet in length. What is the height of the tree.
Let's set up the ratios using similar triangles:
Let "x" be the height of the tree.
Based on the given information, we can set up the following ratios:
(height of the tree) / (length of the tree's shadow) = (person's height) / (person's shadow length)
x/154 = 6/14
Now, we can cross-multiply and solve for "x":
14x = 6 * 154
Dividing both sides by 14:
x = (6 * 154) / 14
x = 66
Therefore, the height of the tree is 66 feet.