A pole that is 3.1 m tall casts a shadow that is 1.39 m long. At the same time, a nearby building casts a shadow that is 36.25 m long. How tall is the building? Round your answer to the nearest meter.

To determine the height of the building using the concept of similar triangles, we can follow these steps:

Given:
- Height of the pole \( h_p = 3.1 \) meters
- Length of the pole's shadow \( s_p = 1.39 \) meters
- Length of the building's shadow \( s_b = 36.25 \) meters

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

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. This gives us the proportion:

\[
\frac{h_p}{s_p} = \frac{h_b}{s_b}
\]

Substituting the given values:

\[
\frac{3.1}{1.39} = \frac{h_b}{36.25}
\]

Solving for \( h_b \):

\[
h_b = \frac{3.1 \times 36.25}{1.39}
\]

First, calculate \( 3.1 \times 36.25 \):

\[
3.1 \times 36.25 = 112.375
\]

Next, divide by 1.39:

\[
h_b = \frac{112.375}{1.39} \approx 80.86
\]

Rounding to the nearest meter:

\[
h_b \approx 81 \text{ meters}
\]

Thus, the height of the building is approximately 81 meters.

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

Here are some related questions you might find interesting:
1. How do similar triangles help in real-world applications like construction?
2. What are other methods to measure the height of tall structures?
3. How does the time of day affect the length of shadows?
4. Can this method be used for objects that are not vertical?
5. What is the role of the sun's angle in shadow length measurement?
6. How can we ensure the accuracy of measurements taken in this way?
7. What are some practical uses of trigonometry in everyday life?
8. How can technology aid in measuring heights and distances accurately?

**Tip:** When using shadows to measure heights, ensure that the surface is flat and the objects are vertical to minimize errors.

Learn how to calculate the height of a building using shadow lengths. Given the height and shadow length of a pole, and the shadow length of the building, solve for the building's height using the concept of similar triangles. Suitable for Grades 7-9.

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