# Flag Pole Estimation Project

## AA Similarity

Q: Why does AA similarity Work?

A: If we know that one angle on each triangle is 90 degrees, and we know one other pair of angles, we can set up a proportion and cross multiply to find the variable!

Q: Where are the two pairs of angles?

A: The right angles (person to ground, flagpole to ground) and the mirror's reflections (eyes to mirror, flagpole top to mirror)

Q: Why does the mirror provide the congruent angle pairs?

A: As long as the mirror is exactly horizontal, the mirror will show an accurate reflection of the top of the flagpole. This will display the "angle" of the person's eyes to the mirror, and then the flagpole to the mirror -this will provide the two pairs which we need in order to solve the proportion.

## The "Pencil-Person" Estimating Technique

The "Pencil to Person" technique has been around for a long time and is simply a estimation trick. For instance, Caleb is 5'5". He stands next to the flag pole. Elizabeth walk far enough away from the flagpole and holds up a pencil, so that Caleb looks as tall as the pencil. Then Elizabeth counts how many pencils it "takes" in order to reach the top. If Caleb is 5'5" and it takes 6 pencils to reach the top, then we simply multiply 65"x 6 and divide by 12 to get 32 1/2 feet in height of the flagpole.

Flag Pole Project