Pete is standing 2 feet away from a mirror on the ground. Pete is 5 feet tall and can just see the top of the tree in the mirror from where he is standing. The mirror is 8 feet away from the base of the tree. how tall is the tree?
What do you mean by "just see"?
Pete has to look up into the mirror, so he is not standing in the way.
If he looks way high into the mirror, the tree is way tall. If he looks just slightly up, the tree is not so tall.
What does he have to look past that blocks his view up to the top of the tree?
To determine the height of the tree, we can use the concept of similar triangles. Let's break down the information given:
1. Pete is standing 2 feet away from a mirror on the ground.
2. Pete is 5 feet tall and can just see the top of the tree in the mirror.
3. The mirror is 8 feet away from the base of the tree.
We can set up a proportion using the similar triangles formed with Pete, the mirror, and the tree. The ratio of Pete's height to his distance from the mirror should be equal to the ratio of the tree's height to its distance from the mirror.
Let's assign variables:
- Pete's height: P
- Pete's distance from the mirror: D
- Tree's height: T
- Tree's distance from the mirror: M
Therefore, we have:
P/D = T/M
From the given information, we know that Pete's height (P) is 5 feet, Pete's distance from the mirror (D) is 2 feet, and the mirror's distance from the tree (M) is 8 feet.
Plugging these values into the proportion, we have:
5/2 = T/8
To solve for T, we can cross-multiply:
5 * 8 = 2 * T
40 = 2T
Now, divide both sides of the equation by 2:
40/2 = T
20 = T
Therefore, the height of the tree is 20 feet.