Question

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.

Answer 1

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.