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To find the height of the building, we can use similar triangles. Since the pole and its shadow form a triangle with the sun, and the building and its shadow form a similar triangle with the same angle of sunlight, the ratios of corresponding sides of these triangles will be equal.

Given:
- Height of the pole \( = 3.2 \, \text{m} \)
- Shadow of the pole \( = 1.64 \, \text{m} \)
- Shadow of the building \( = 48.5 \, \text{m} \)
  
Let \( h \) be the height of the building.

Using the similarity of the triangles:
\[
\frac{\text{Height of Pole}}{\text{Shadow of Pole}} = \frac{\text{Height of Building}}{\text{Shadow of Building}}
\]

Substitute the known values:
\[
\frac{3.2}{1.64} = \frac{h}{48.5}
\]

Now, solve for \( h \):
1. Cross multiply:
   \[
   3.2 \times 48.5 = 1.64 \times h
   \]

2. Simplify:
   \[
   155.2 = 1.64 \times h
   \]

3. Divide by 1.64 to find \( h \):
   \[
   h = \frac{155.2}{1.64}
   \]

4. Calculate \( h \):
   \[
   h \approx 94.7
   \]

Rounding to the nearest meter, the height of the building is approximately \( 95 \, \text{m} \).

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Would you like more details on any step, or do you have further questions?

### Related Questions
1. How do similar triangles help in solving problems involving heights and shadows?
2. How would the height of the building change if the pole had a different height but the same shadow length?
3. How do you set up proportions in similar triangle problems with different configurations?
4. What are some real-life applications of similar triangles outside of measuring heights?
5. How would you solve this problem if you only knew the angles involved?

### Tip
When working with similar triangles, always ensure that the corresponding sides are used in the ratio correctly to avoid errors in setting up proportions.

A pole that is 3.2 m tall casts a shadow that is 1.64 m long. At the same time, a nearby building casts a shadow that is 48.5 m long. How tall is the building? Round your answer to the nearest meter.

Learn how to calculate the height of a building using the concept of similar triangles and proportions. This problem involves a 3.2 m tall pole casting a 1.64 m shadow and a building casting a 48.5 m shadow. Suitable for students in Grades 7-10.

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