We can solve this problem using the concept of similar triangles. Here's a breakdown of the situation:

Step 1: Understanding the setup

• Abby stands 9.45 meters away from the building.
• She walks 2.75 meters further from the mirror, so her total distance from the building is $9.45 + 2.75 = 12.2 \, \text{meters}$.
• The distance from Abby’s eyes to the ground is 1.55 meters.
• The angle of reflection allows her to see the top of the school in the mirror.

We can visualize the situation as a right triangle with the following features:

• The school’s height forms one leg of the triangle.
• The total distance Abby stands from the building (12.2 meters) forms the base of the triangle.
• The height from Abby’s eyes to the ground (1.55 meters) forms the other leg.

Step 2: Set up the proportion using similar triangles

Since the angle of reflection is equal to the angle of incidence, the triangles formed by Abby, the building, and the mirror are similar. Therefore, we can set up a proportion between the corresponding sides of the triangles:

$\frac{\text{height of school}}{\text{distance from the building}} = \frac{\text{height of Abby’s eyes}}{\text{distance from Abby to the mirror}}$

Substitute the known values: $\frac{h}{12.2} = \frac{1.55}{9.45}$

Where:

• $h$ is the height of the school.
• 1.55 meters is the height from Abby’s eyes to the ground.
• 9.45 meters is the distance from Abby to the mirror (before walking the extra 2.75 meters).

Step 3: Solve for $h$

First, calculate the right side of the proportion: $\frac{1.55}{9.45} \approx 0.1647$

Now solve for $h$: $h = 12.2 \times 0.1647 \approx 2.01 \, \text{meters}$

Thus, the height of the school is approximately 2.01 meters.

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Would you like more details or have any questions about this method? Here are some related questions you might find interesting:

1. How would the result change if Abby's eyes were at a different height?
2. What would happen if Abby stood farther from the building?
3. How can we calculate the angle of elevation to the top of the school from Abby’s position?
4. How could we use this same method to measure the height of a tree or other object outdoors?
5. What assumptions are we making about the mirror’s placement in this problem?

Tip: In problems involving similar triangles, always check that the triangles are indeed similar by ensuring that corresponding angles are equal, as in this case where the angle of incidence equals the angle of reflection.