To solve the problem, we use the principles of similar triangles. Here is a step-by-step breakdown of the solution:

Step 1: Understand the setup

• $h$: The height of the school building (to be determined).
• $d_1 = 11.35 \, \text{m}$: Distance from the school to the mirror.
• $d_2 = 2.05 \, \text{m}$: Distance from the mirror to Fawzia.
• $h_{\text{Fawzia}} = 1.25 \, \text{m}$: Height of Fawzia's eyes from the ground.

The mirror creates similar triangles:

1. The large triangle formed by the school building, the mirror, and the top of the building.
2. The smaller triangle formed by Fawzia, the mirror, and the line of sight to her eyes.

Step 2: Set up the similarity ratio

The heights and corresponding distances of the triangles are proportional: $\frac{h}{d_1} = \frac{h_{\text{Fawzia}}}{d_2}.$

Step 3: Solve for $h$

Rearranging the formula: $h = \frac{h_{\text{Fawzia}}}{d_2} \cdot d_1.$

Substitute the known values: $h = \frac{1.25}{2.05} \cdot 11.35.$

First, calculate the fraction: $\frac{1.25}{2.05} \approx 0.6098.$

Then, multiply by $11.35$: $h \approx 0.6098 \cdot 11.35 \approx 6.92 \, \text{m}.$

Final Answer:

The height of the school building is approximately 6.92 meters.

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Would you like further details on any step?
Here are 5 related questions to deepen understanding:

1. What assumptions are made in this problem regarding the reflection in the mirror?
2. How would the result change if the mirror were not flat on the ground?
3. What are other methods to measure the height of tall objects indirectly?
4. How can trigonometry be applied to solve similar problems?
5. Why is it important that the top of the school is directly visible in the mirror?

Tip: When solving problems involving similar triangles, carefully label the corresponding sides and angles to avoid confusion.