A pole that is 3.3 m tall casts a shadow that is 1.02 m long. At the same time, a nearby building casts a shadow that is 39.75 m long. How tall is the building? Round your answer to the nearest meter.

To determine the height of the building, we can use the concept of similar triangles. The ratio of the height of the pole to the length of its shadow is equal to the ratio of the height of the building to the length of its shadow.

Given:
- Height of the pole \( h_p = 3.3 \) meters
- Length of the pole's shadow \( s_p = 1.02 \) meters
- Length of the building's shadow \( s_b = 39.75 \) meters

Let \( h_b \) be the height of the building.

We can set up the proportion:
\[
\frac{h_p}{s_p} = \frac{h_b}{s_b}
\]

Substitute the known values:
\[
\frac{3.3}{1.02} = \frac{h_b}{39.75}
\]

Solving for \( h_b \):
\[
h_b = \frac{3.3 \times 39.75}{1.02}
\]

First, calculate \( 3.3 \times 39.75 \):
\[
3.3 \times 39.75 = 131.175
\]

Then, divide by 1.02:
\[
h_b = \frac{131.175}{1.02} = 128.6014705882353
\]

Rounding to the nearest meter:
\[
h_b \approx 129 \text{ meters}
\]

Thus, the height of the building is approximately 129 meters.

Would you like more details on the calculation or have any questions?

Here are some related questions you might find interesting:
1. What is the importance of similar triangles in real-life applications?
2. How can we determine the height of an object using its shadow and a reference object?
3. Can we use this method at different times of the day?
4. What are other methods to measure the height of tall buildings?
5. How does the angle of elevation affect the length of the shadow?
6. What tools can help in accurately measuring shadows?
7. How can trigonometry be applied to solve similar problems?
8. What are some challenges in measuring shadows accurately?

**Tip:** Always ensure that measurements are taken on level ground to maintain the accuracy of shadow length calculations.

Learn how to calculate the height of a building using shadow lengths. This problem involves applying the concept of similar triangles to find the building's height based on the shadow lengths of a nearby pole and the building itself. Suitable for students in Grades 7-9.

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