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 two triangles formed in the picture above are similar.

If the mirror is 12 feet away from the base of the tree, how tall is the tree?

18

16 To find the height of the tree, we can set up a proportion using the similar triangles.

Let's call the height of the tree 'h'.

In the first triangle formed by Pete's height and the distance between him and the mirror, we have a ratio:

Pete's height / Distance to the mirror = h / (h + 2)

In the second triangle formed by the height of the tree and the distance between the mirror and the tree, we have:

Height of the tree / Distance to the tree = h / 12

Since the two triangles are similar, we can set up the proportion:

(Pete's height) / (Distance to the mirror) = (Height of the tree) / (Distance to the tree)

Plugging in the given values:

5 / 2 = h / 12

Now, we can solve for h by cross-multiplying:

5 * 12 = 2 * h

60 = 2h

Dividing by 2 on both sides:

h = 30

Therefore, the tree is 30 feet tall.

If the two triangles are similar (and they are -- why?) then if the tree has height h,

h/12 = 5/2