Question

A pole that is 3.5m tall casts a shadow that is 1.45m long. At the same time, a nearby building casts a shadow that is 40.75m long. How tall is the building? Round your answer to the nearest meter.

Answer 1

To solve this problem, we can use the concept of similar triangles. The ratio of the height of the pole to the length of its shadow will be the same as the ratio of the height of the building to the length of its shadow.

Let's set up the proportion:

(height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)

Substituting the given values:

3.5m / 1.45m = (height of building) / 40.75m

Now, we can solve for the height of the building:

(height of building) = (3.5m / 1.45m) * 40.75m

Calculating this expression will give us the height of the building. Rounding the answer to the nearest meter will give us the final results

Answer 2

The height of the building is determined using the similar triangles method by setting up a ratio using the height and shadow length of a known pole and the shadow length of the building. After calculating, the building is approximately 99 meters tall.

Step-by-step explanation:

Proportion to Determine Building Height

To find the height of a building based on a known pole height and shadow lengths, we use the concept of similar triangles. In this case, the ratio of the pole's height to its shadow length should be the same as the ratio of the building's height to its shadow length.

• Let H represent the height of the building.
• Ratio for pole: Height/Shade = 3.5/1.45
• Ratio for building: H/40.75 must equal 3.5/1.45
• Solve for H: (3.5/1.45) = H/40.75

By solving the proportion (3.5/1.45) = H/40.75, we find the height of the building.

H = (3.5/1.45) * 40.75 ≈ 98.57 meters

When rounding to the nearest meter, the building is approximately 99 meters tall.